???global.info.a_carregar???
Identification

Personal identification

Full name
Pedro Miguel Nunes da Rosa Dias Duarte

Citation names

  • Duarte, Pedro

Author identifiers

Ciência ID
8010-2A22-AB6E
ORCID iD
0000-0002-1838-3770
Google Scholar ID
Pedro Duarte
Scopus Author Id
55984033100
Education
Degree Classification
2017
Concluded
 Matemática (Título de Agregado)
Universidade de Lisboa Faculdade de Ciências, Portugal
1989 - 1993
Concluded
 Matemática (Doctor)
Major in Sistemas Dinâmicos
Instituto Nacional de Matemática Pura e Aplicada, Brazil
"Existência de Muitas Ilhas Eli´ticas para a Fami´lia Canônica de Transformações que Preservam Área." (THESIS/DISSERTATION)
1993
Concluded
 Matemática (Postgraduate Certificate)
Major in Sistemas DInâmicos
KTH Institutionen för farkost och flyg, Sweden
1980 - 1985
Concluded
 Matemática (Licenciatura)
Major in Matemática Pura
Universidade de Lisboa Faculdade de Ciências, Portugal
 19
Affiliation

Teaching in Higher Education

Category
Host institution 		Employer
2024/02/01 - Current Full Professor (University Teacher) Universidade de Lisboa Faculdade de Ciências, Portugal
Universidade de Lisboa Faculdade de Ciências, Portugal
2018/05/01 - 2024/01/31 Associate Professor (University Teacher) Universidade de Lisboa Faculdade de Ciências, Portugal
2000 - 2018 Assistant Professor (University Teacher) Universidade de Lisboa Faculdade de Ciências, Portugal
1995/11/01 - 2000/10/01 Assistant Professor (University Teacher) Universidade de Lisboa Instituto Superior Técnico, Portugal
1993/05/01 - 1995/11/01 Assistant Professor (University Teacher) Universidade de Lisboa Faculdade de Ciências, Portugal
1985/10/01 - 1993/05/01 Assistant (University Teacher) Universidade de Lisboa Faculdade de Ciências, Portugal
Projects

Contract

Designation Funders
2018/09/01 - 2022/07/31 Novas Tendências em expoentes de Lyapunov
PTDC/MAT-PUR/29126/2017
FCiênciasID Associação para a Investigação e Desenvolvimento de Ciências, Portugal

Universidade de Lisboa Centro de Matematica Aplicada à Previsão e Decisão Económica, Portugal

Universidade do Minho, Portugal

Universidade da Beira Interior, Portugal
Fundação para a Ciência e a Tecnologia
Ongoing
2010/01/01 - 2013/07/31 Aleatoriedade em Sistemas Dinâmicos Determinísticos e Aplicações
PTDC/MAT/105448/2008
Universidade de Lisboa Centro de Matematica Aplicada à Previsão e Decisão Económica, Portugal

Fundação da Faculdade de Ciências da Universidade de Lisboa, Portugal
Fundação para a Ciência e a Tecnologia
Concluded
Outputs

Publications

Book
  1. Duarte, Pedro; Klein, Silvius. Continuity of the Lyapunov exponents of linear cocycles. Rio de Janeiro, Brazil: Associação Instituto de Matemática Pura e Aplicada- IMPA. 2017.
    Published
  2. Duarte, Pedro; Klein, Silvius. Lyapunov Exponents of Linear Cocycles. Atlantis Press. 2016.
    10.2991/978-94-6239-124-6
Book chapter
  1. Del Magno, Gianluigi; Lopes Dias, João; Duarte, Pedro; Gaivão, José Pedro; Pinheiro, Diogo. "Polygonal Billiards with Strongly Contractive Reflection Laws: A Review of Some Hyperbolic Properties". In Difference Equations, Discrete Dynamical Systems and Applications, 179-190. Springer Berlin Heidelberg, 2016.
    10.1007/978-3-662-52927-0_14
  2. Duarte, Pedro; Torres, Maria Joana. "Stability of Non-deterministic Systems". In From Particle Systems to Partial Differential Equations II, 193-207. Springer International Publishing, 2015.
    10.1007/978-3-319-16637-7_6
  3. Duarte, Pedro. "Hamiltonian Systems on Polyhedra". In Springer Proceedings in Mathematics, 257-274. Springer Berlin Heidelberg, 2011.
    10.1007/978-3-642-14788-3_21
Conference paper
  1. Duarte, P.; Nunes, I.; Neto, J.P.; Chambel, T.. "Enhancing Modularity and Feedback in Computer Aided Assessment". 2006.
    10.1109/cic.2006.36
Edited book
  1. Bessa, Mário; Lopes Dias, João; Bezerra, Jamerson; Mauricio Poletti; Ao Cai; Anders Karlsson; Reza Mohammadpour; Paulo Varandas; Adriana Sánchez, ed. New Trends in Lyapunov Exponents. Springer International Publishing. 2023.
    Published • 10.1007/978-3-031-41316-2
Journal article
  1. Pedro Duarte; Catalina Freijo. "Continuity of the Lyapunov exponents of non-invertible random cocycles with constant rank". Nonlinearity (2024): http://dx.doi.org/10.1088/1361-6544/ad72c7.
    10.1088/1361-6544/ad72c7
  2. Bezerra, Jamerson; Cai, Ao; Duarte, Pedro; Freijo, Catalina; Klein, Silvius. "A dynamical Thouless formula". Advances in Mathematics 438 (2024): 109446. http://dx.doi.org/10.1016/j.aim.2023.109446.
    10.1016/j.aim.2023.109446
  3. Bezerra, Jamerson; Duarte, Pedro. "Upper Bound on the Regularity of the Lyapunov Exponent for Random Products of Matrices". Communications in Mathematical Physics 403 2 (2023): 829-875. http://dx.doi.org/10.1007/s00220-023-04815-5.
    10.1007/s00220-023-04815-5
  4. Ao Cai; Pedro Duarte; Silvius Klein. "Furstenberg Theory of Mixed Random-Quasiperiodic Cocycles". Communications in Mathematical Physics (2023): https://doi.org/10.1007/s00220-023-04726-5.
    10.1007/s00220-023-04726-5
  5. Hassan Najafi Alishah; Pedro Duarte; Telmo Peixe. "Asymptotic dynamics of Hamiltonian polymatrix replicators". Nonlinearity (2023): https://doi.org/10.1088/1361-6544/acd043.
    10.1088/1361-6544/acd043
  6. Alexandre Baraviera; Pedro Duarte; Maria Joana Torres. "Synchronization of coupled map lattices". Proceedings of the Edinburgh Mathematical Society (2023): 1-21. http://dx.doi.org/10.1017/s0013091523000081.
    10.1017/s0013091523000081
  7. Pedro Duarte; Silvius Klein; Mauricio Poletti. "Hölder continuity of the Lyapunov exponents of linear cocycles over hyperbolic maps". Mathematische Zeitschrift 302 4 (2022): 2285-2325. http://dx.doi.org/10.1007/s00209-022-03147-9.
    10.1007/s00209-022-03147-9
  8. Ao Cai; Pedro Duarte; Silvius Klein. "Mixed Random-Quasiperiodic Cocycles". Bulletin of the Brazilian Mathematical Society, New Series 53 4 (2022): 1469-1497. http://dx.doi.org/10.1007/s00574-022-00313-9.
    10.1007/s00574-022-00313-9
  9. Baraviera, Alexandre; Duarte, Pedro; Torres, Maria Joana. "Stationary measures on infinite graphs". Communications in Contemporary Mathematics (2021): 2150025. http://dx.doi.org/10.1142/s0219199721500255.
    10.1142/s0219199721500255
  10. Del Magno, Gianluigi; Lopes Dias, João; Duarte, Pedro; Gaivão, José Pedro. "Hyperbolic Polygonal Billiards Close to 1-Dimensional Piecewise Expanding Maps". Journal of Statistical Physics 182 1 (2021): http://dx.doi.org/10.1007/s10955-020-02673-2.
    10.1007/s10955-020-02673-2
  11. Duarte, Pedro; Torres, Maria Joana. "Isospectral reduction in infinite graphs". Journal of Spectral Theory 10 3 (2020): 955-989. http://dx.doi.org/10.4171/jst/318.
    10.4171/jst/318
  12. Gianluigi Del Magno; João Lopes Dias; Pedro Duarte; José Pedro Gaivão. "The attractor of piecewise expanding maps of the interval". Stochastics and Dynamics 20 02 (2020): 2050009-2050009. http://dx.doi.org/10.1142/s0219493720500094.
    10.1142/s0219493720500094
  13. Najafi Alishah, Hassan; Duarte, Pedro; Peixe, Telmo. "Asymptotic Poincaré maps along the edges of polytopes". Nonlinearity 33 1 (2019): 469-510. http://dx.doi.org/10.1088/1361-6544/ab49e6.
    10.1088/1361-6544/ab49e6
  14. Duarte, Pedro; Klein, Silvius. "Large Deviations for Products of Random Two Dimensional Matrices". Communications in Mathematical Physics 375 3 (2019): 2191-2257. http://dx.doi.org/10.1007/s00220-019-03586-2.
    10.1007/s00220-019-03586-2
  15. Duarte, Pedro; Klein, Silvius. "Continuity, positivity and simplicity of the Lyapunov exponents for quasi-periodic cocycles". Journal of the European Mathematical Society 21 7 (2019): 2051-2106. http://dx.doi.org/10.4171/jems/880.
    10.4171/jems/880
  16. Baraviera, Alexandre; Duarte, Pedro. "Approximating Lyapunov Exponents and Stationary Measures". Journal of Dynamics and Differential Equations 31 1 (2019): 25-48. http://dx.doi.org/10.1007/s10884-018-9724-5.
    10.1007/s10884-018-9724-5
  17. Duarte, Pedro; Klein, Silvius; Santos, Manuel. "A random cocycle with non Hölder Lyapunov exponent". Discrete & Continuous Dynamical Systems - A 39 8 (2019): 4841-4861. http://dx.doi.org/10.3934/dcds.2019197.
    10.3934/dcds.2019197
  18. Duarte, Pedro; Klein, Silvius. "Topological obstructions to dominated splitting for ergodic translations on the higher dimensional torus". Discrete & Continuous Dynamical Systems - A 38 11 (2018): 5379-5387. http://dx.doi.org/10.3934/dcds.2018237.
    10.3934/dcds.2018237
  19. DEL MAGNO, GIANLUIGI; LOPES DIAS, JOÃO; DUARTE, PEDRO; GAIVÃO, JOSÉ PEDRO. "Hyperbolic polygonal billiards with finitely many ergodic SRB measures". Ergodic Theory and Dynamical Systems 38 6 (2017): 2062-2085. http://dx.doi.org/10.1017/etds.2016.119.
    10.1017/etds.2016.119
  20. Duarte, Pedro; Gaivão, José Pedro; Soufi, Mohammad. "Hyperbolic billiards on polytopes with contracting reflection laws". Discrete & Continuous Dynamical Systems - A 37 6 (2017): 3079-3109. http://dx.doi.org/10.3934/dcds.2017132.
    10.3934/dcds.2017132
  21. Duarte, Pedro; Klein, Silvius. "Large deviation type estimates for iterates of linear cocycles". Stochastics and Dynamics 16 03 (2016): 1660010. http://dx.doi.org/10.1142/s0219493716600108.
    10.1142/s0219493716600108
  22. Alishah, Hassan Najafi; Duarte, Pedro; Peixe, Telmo. "Conservative and dissipative polymatrix replicators". Journal of Dynamics and Games 2 2 (2015): 157-185. http://dx.doi.org/10.3934/jdg.2015.2.157.
    10.3934/jdg.2015.2.157
  23. Alishah, Hassan Najafi; Duarte, Pedro. "Hamiltonian evolutionary games". Journal of Dynamics and Games 2 1 (2015): 33-49. http://dx.doi.org/10.3934/jdg.2015.2.33.
    10.3934/jdg.2015.2.33
  24. Duarte, Pedro; Torres, Maria Joana. "Eigenvectors of isospectral graph transformations". Linear Algebra and its Applications 474 (2015): 110-123. http://dx.doi.org/10.1016/j.laa.2015.01.038.
    10.1016/j.laa.2015.01.038
  25. Duarte, Pedro; Torres, Maria Joana. "r-Regularity". Journal of Mathematical Imaging and Vision 51 3 (2014): 451-464. http://dx.doi.org/10.1007/s10851-014-0535-y.
    10.1007/s10851-014-0535-y
  26. Del Magno, Gianluigi; Lopes Dias, João; Duarte, Pedro; Pedro Gaivão, José. "Ergodicity of polygonal slap maps". Nonlinearity 27 8 (2014): 1969-1983. http://dx.doi.org/10.1088/0951-7715/27/8/1969.
    10.1088/0951-7715/27/8/1969
  27. Duarte, Pedro; Klein, Silvius. "Positive Lyapunov Exponents for Higher Dimensional Quasiperiodic Cocycles". Communications in Mathematical Physics 332 1 (2014): 189-219. http://dx.doi.org/10.1007/s00220-014-2082-1.
    10.1007/s00220-014-2082-1
  28. Duarte, Pedro; Klein, Silvius. "Continuity of the Lyapunov Exponents for Quasiperiodic Cocycles". Communications in Mathematical Physics 332 3 (2014): 1113-1166. http://dx.doi.org/10.1007/s00220-014-2068-z.
    10.1007/s00220-014-2068-z
  29. Del Magno, Gianluigi; Lopes Dias, João; Duarte, Pedro; Gaivão, José Pedro; Pinheiro, Diogo. "SRB Measures for Polygonal Billiards with Contracting Reflection Laws". Communications in Mathematical Physics 329 2 (2014): 687-723. http://dx.doi.org/10.1007/s00220-014-1960-x.
    10.1007/s00220-014-1960-x
  30. Duarte, Pedro; Torres, Maria Joana. "Smoothness of Boundaries of Regular Sets". Journal of Mathematical Imaging and Vision 48 1 (2012): 106-113. http://dx.doi.org/10.1007/s10851-012-0397-0.
    10.1007/s10851-012-0397-0
  31. Duarte, Pedro; Peixe, Telmo. "Rank of stably dissipative graphs". Linear Algebra and its Applications 437 10 (2012): 2573-2586. http://dx.doi.org/10.1016/j.laa.2012.06.015.
    10.1016/j.laa.2012.06.015
  32. Del Magno, Gianluigi; Lopes Dias, João; Duarte, Pedro; Pedro Gaivão, José; Pinheiro, Diogo. "Chaos in the square billiard with a modified reflection law". Chaos: An Interdisciplinary Journal of Nonlinear Science 22 2 (2012): 026106. http://dx.doi.org/10.1063/1.3701992.
    10.1063/1.3701992
  33. Duarte, Pedro; Torres, Maria Joana. "A Discrete Faà di Bruno's Formula, Contribution to Discrete Mathematics". CONTRIBUTION TO DISCRETE MATHEMATICS 7 2 (2012): 72-83. http://hdl.handle.net/10515/sy5fn1173.
    Published
  34. Duarte, Pedro; Torres, Maria Joana. "A discrete Faà di Bruno's formula". Contributions to Discrete Mathematics 7 2 (2012): 72-83.
    Published
  35. Baraviera, Alexandre T; Dias, João Lopes; Duarte, Pedro. "On the Herman–Avila–Bochi formula for Lyapunov exponents of {\rm SL}(2,\mathbb{R}) -cocycles". Nonlinearity 24 9 (2011): 2465-2476. http://dx.doi.org/10.1088/0951-7715/24/9/004.
    10.1088/0951-7715/24/9/004
  36. Bessa, Mário; Duarte, Pedro. "Abundance of elliptic dynamics on conservative three-flows". Dynamical Systems 23 4 (2008): 409-424. http://dx.doi.org/10.1080/14689360802162872.
    10.1080/14689360802162872
  37. DUARTE, P.; Duarte, Pedro. "Elliptic isles in families of area-preserving maps". Ergodic Theory and Dynamical Systems 28 06 (2008): 1781. http://dx.doi.org/10.1017/s0143385707000983.
    10.1017/s0143385707000983
  38. Duarte, P; Torres, M J. "Spectral stability of Markov systems". Nonlinearity 21 3 (2008): 381-397. http://dx.doi.org/10.1088/0951-7715/21/3/001.
    10.1088/0951-7715/21/3/001
  39. DUARTE, P.; TORRES, M. J.; Duarte, Pedro. "Combinatorial stability of non-deterministic systems". Ergodic Theory and Dynamical Systems 26 01 (2005): 93. http://dx.doi.org/10.1017/s0143385705000301.
    10.1017/s0143385705000301
  40. DUARTE, PEDRO. "Persistent homoclinic tangencies for conservative maps near the identity". Ergodic Theory and Dynamical Systems 20 2 (2000): 393-438. http://dx.doi.org/10.1017/s0143385700000195.
    10.1017/s0143385700000195
  41. Duarte, Pedro. "Abundance of elliptic isles at conservative bifurcations". Dynamics and Stability of Systems 14 4 (1999): 339-356. http://dx.doi.org/10.1080/026811199281930.
    10.1080/026811199281930
  42. Duarte, Pedro; Fernandes, Rui L.; Oliva, Waldyr M.. "Dynamics of the Attractor in the Lotka–Volterra Equations". Journal of Differential Equations 149 1 (1998): 143-189. http://dx.doi.org/10.1006/jdeq.1998.3443.
    10.1006/jdeq.1998.3443
  43. Duarte, Pedro. "Plenty of elliptic islands for the standard family of area preserving maps". Annales de l'Institut Henri Poincaré C, Analyse non linéaire 11 4 (1994): 359-409. http://dx.doi.org/10.1016/s0294-1449(16)30180-9.
    10.1016/s0294-1449(16)30180-9
Activities

Oral presentation

Presentation title Event name
Host (Event location)
2024/09/18 Regularity of the Lyapunov Exponents of two dimensional cocycles Joint 2nd Workshop Nordestino de Sistemas Dinâmicos and 3rd Jangada Dinâmica
Universidade Federal do Ceará (Fortaleza, Brazil)
2024/07/10 Lyapunov exponents of random GL(2,R) cocycles. ENSPM 2024, Sessão Temática Low Dimensional Dynamical Systems
Universidade do Minho (Braga, Portugal)
2024/07/02 On the Lyapunov exponents of random Mat(2,R) cocycles XXI International Congress of mathematical Physics, Dynamical Systems Thematic Session.
Université de Strasbourg (Strasbourg, France)
2023/11/03 A Dynamical Thouless Formula Invited seminar at Soochow University
Soochow University (Soochow, China)
2023/10/31 Regularity of the Lyapunov Exponents of SL(2)-random cocycles Invited seminar at Chern Institute of Mathematics
University of Nankai (Nankai, China)
2023/10/29 A Dynamical Thouless Formula 2023 Symposium on the Theories and Algorithms of Dynamical Systems and related problems
Nanjing University (Nanjing, China)
2023/04/12 Positivity and Continuity of the Lyapunov Exponents of 2d cocycles Two Dimensional Maps, Workshop II
Institut Mittag-Leffler (Stockholm, Sweden)
2022/10/25 Regularity of the Lyapunov exponents of random SL(2, R)-cocycles , International Conference on Dynamical Systems, Celebrating the 60 th Birthday of Marcelo Viana
IMPA, Instituto de Matemática Pura e Aplicada (Rio de Janeiro)
2022/09/09 Stability of the Lyapunov exponents of randomly perturbed quasi-periodic cocycles 8th IST-IME Meeting
IST, Instituto Superior Técnico (Lisboa, Portugal)
2022/08/19 Sharp regularity of the Lyapunov exponents of random cocycles Encontro Conjunto Brasil- Portugal em Matemática
Universidade Federal da Bahia (São Salvador da Bahia, Brazil)
2022/04/22 Regularity of the Lyapunov exponents of random linear cocycles Séminaire de Systèmes Dynamiques
Institut de Mathématiques de Jussieu-PRG (Paris, France)
2021/09 Statistical Properties of Linear Cocycles and Quantitative Continuity of Lyapunov Exponents 2nd Workshop on Wild Dynamics, São Miguel, Açores, September 2021
Institut de mathématiques de Jussieu Paris Rive Gauche
2020/11/27 Random perturbations of quasi-periodic cocycles Séminaire de Systèmes Dynamiques
Institut de Mathématiques de Jussieu -Paris Rive Gauche
2020/10/14 Continuity of Lyapunov exponents for mixed random quasi-periodic cocycles Jorge Rocha 60 anos, Symposium in Dynamical Systems
Universidade do Porto Faculdade de Ciências (Porto, Portugal)
2020/04/17 Hölder continuity of the Lyapunov exponent for linear cocycles over hyperbolic dynamical systems Resistência Dinâmica: Conferência de homenagem aos 80 anos de Jacob Palis
PUC-Rio de Janeiro (Rio de Janeiro, Brazil)
2020/02/03 Lyapunov Exponents of quasi-periodic cocycles with random noise In the shadow of Lyapunov exponents (2nd edition)
PUC-Rio de Janeiro (Rio de Janeiro, Brazil)
2019/01 The Avalanche Principle À sombra de expoentes de Lyapunov
PUC-Rio de Janeiro (Rio de Janeiro, Brazil)
2018/09/06 Large deviations for random 2-dimensional cocycles Workshop on Quasi-periodic Dynamics and Schrödinger operators
Nanjing University (Nanjing, China)
2018/02/21 Regularity of Lyapunov exponents of random linear cocycles Probability and Applications Seminar
Queen Mary University of London (Londres, United Kingdom)
2017/08 Limitations on the regularity of Lyapunov exponents of linear cocycles Sessão temática de Sistemas Dinâmicos, 31º Colóquio Brasileiro de Matemática
Instituto de Matemática Pura e Aplicada (Rio de Janeiro, Brazil)
2016/08 Isospectral Reduction in Infinite Graphs Analysis Seminar
NTNU Trondheim Univerisity (Tronheim, Norway)
2016/03 Large deviation estimates for mixing Markov systems Analysis Seminar
NTNU Trondheim Univerisity (Tronheim, Norway)
2015/10/14 On the continuity of the Lyapunov exponents Après midi, seminaire systemes dynamiques
Institut Galilée, Université de Paris 13 (Paris, France)
2015/09 Dissipative Polygonal Billiards Analysis Seminar
NTNU Trondheim Univerisity (Trondheim, Norway)
2015/06 Large deviation estimates for Markovian cocycles AMS-EMS-SPM international meeting
Universidade do Porto Faculdade de Ciências (Porto, Portugal)
2015/03 Large deviation estimates for mixing Markov cocycles Analysis Seminar
NTNU Trondheim Univerisity (Trondheim, Norway)
2014/10 Continuity of Lyapunov Exponents 5th Iberian Mathematical Meeting
Universidade de Aveiro (Aveiro, Portugal)
2014/02 Hyperbolic Polyhedral Billiards EURO Mini-conference on Optimization in the Natural Sciences
Universidade de Aveiro (Aveiro, Portugal)
2013/09 Dynamical embeddings in Lotka-Volterra Systems DGS 2013 - International Conference Planet Earth, Dynamics, Games and Science
Fundação Calouste Gulbenkian (Lisboa, Portugal)
2012/09 Dissipative Polygonal Billiards 4th IST-IME Meeting, Lisboa
IST Universidade de Lisboa (Lisboa, Portugal)
2012/08 Dissipative polygonal billiards Montevideo Dynamical Systems Conference 2012
Universidad de la Republica Uruguay (Montevideo, Uruguay)
2011/09 Morse Landscapes Elementary Geometry from an Advanced Point of View
Universidade de Aveiro (Aveiro, Portugal)
2010/06 Lyapunov Morse Functions on Flag Manifolds Sessão temática de Sistemas Dinâmicos ENSPM 2010
Instituto Politécnico de Leiria (Leiria, Portugal)
2009/09 Produtos Aleatórios de Matrizes Seminário de Sistemas Dinâmicos
UFRGS Universidade Federal do Rio Grande do Sul (Porto Alegre, Brazil)

Supervision

Thesis Title
Role 		Degree Subject (Type)
Institution / Organization
2019 - 2022 A Geometric Avalanche Principle
Supervisor
 Matemática (PhD)
Universidade de Lisboa Faculdade de Ciências, Portugal
2018 - 2018 A geometrical point of view for the noncommutative ergodic theorems
Co-supervisor
 Matemática (Master)
Universidade de Lisboa Faculdade de Ciências, Portugal
2013 - 2013 Teorema da estrutura de Furstenberg: demonstração e redução ao nível Www
Supervisor
 Matemática (Master)
Universidade de Lisboa Faculdade de Ciências, Portugal
2010 - 2012 Medida de Erdös: Uma Introdução
Supervisor
 Matemática (Master)
Universidade de Lisboa Faculdade de Ciências, Portugal
2011 - 2011 Lotka-Volterra systems and polymatrix replicators
Supervisor
 Matemática (PhD)
Universidade de Lisboa Faculdade de Ciências, Portugal
2008 - 2010 Sistemas Lotka-Volterra Dissipativos
Supervisor
 Matemática (Master)
Universidade de Lisboa Faculdade de Ciências, Portugal
2006 - 2008 Templates e Elos de Órbitas Periódicas em Fluxos de Dimensão 3
Supervisor
 Matemática (Master)
Universidade de Lisboa Faculdade de Ciências, Portugal
2004 - 2004 Markov Chains Close to Maps on Compact Manifolds
Supervisor
 Matemática (PhD)
Universidade de Lisboa, Portugal

Event organisation

Event name
Type of event (Role) 		Institution / Organization
2024/05/27 - 2024/05/29 LxDS Spring School 2024, Mini-escola de Sistemas Dinâmicos (2024/05/27 - 2024/05/29)
Workshop (Co-organisor)
 ISEG Lisbon School of Economics and Management, Portugal
2022/02/07 - 2022/02/11 New trends in Lyapunov exponents (2022/02/07 - 2022/02/11)
Workshop (Member of the Organising Committee)
 ISEG Lisbon School of Economics and Management, Portugal
2021/10/18 - 2021/10/22 LxDS mini-course on Determinantal Point Processes (2021/10/18 - 2021/10/22)
Workshop (Co-organisor)
 Universidade de Lisboa Faculdade de Ciências, Portugal
2021/09 - 2021/09 2nd Workshop on Wild Dynamics, São Miguel, Açores, September 2021 (2021/09 - 2021/09)
Workshop (Co-organisor)
 Institut de mathématiques de Jussieu Paris Rive Gauche, France
2020/07/07 - 2020/07/07 9th One Day Meeting on Dynamical Systems - New trends in Lyapunov Exponents (2020/07/07 - 2020/07/07)
Conference (Co-organisor)
 Universidade de Lisboa Faculdade de Ciências, Portugal
2019/05/29 - 2019/05/31 LxDS Spring School 2019 (2019/05/29 - 2019/05/31)
Workshop (Co-organisor)
2018/05/28 - 2018/05/30 LxDS Spring School 2018, May 28-30, 2018 (2018/05/28 - 2018/05/30)
Workshop (Co-organisor)
 ISEG Lisbon School of Economics and Management, Portugal
2018/05/22 - 2018/05/22 8th One Day Meeting on Dynamical Systems (2018/05/22 - 2018/05/22)
Conference
 Universidade de Lisboa Faculdade de Ciências, Portugal
2016/03/04 - 2016/03/04 7th One Day Meeting on Dynamical Systems, March 4, 2016 (2016/03/04 - 2016/03/04)
Conference (Co-organisor)
 Universidade de Lisboa Faculdade de Ciências, Portugal

Jury of academic degree

Topic
Role 		Candidate name (Type of degree)
Institution / Organization
2020/06 Invariant Manifolds of homoclinic orbits: super homoclinic and multi-pulse homoclinic loops
(Thesis) Main arguer
 Sajjad Bakrani Balani (PhD)
Imperial College - Chelsea and Westminster Campus, United Kingdom
2018/03 Statistical Instability for Rovella Maps
(Thesis) Main arguer
 Muhammad Ali Khan (PhD)
Universidade do Porto Faculdade de Ciências, Portugal
2017/03 Asymptotic Behavior of Compact Skew-product Semiflows on Hilbert Spaces
(Thesis) Main arguer
 Maria Glória Carvalho (PhD)
Universidade do Porto Faculdade de Ciências, Portugal
2015/12 Systems of Iterative Functional Equations: Theory and Applications
(Thesis) Main arguer
 Maria Cristina Serpa (PhD)
Universidade de Lisboa Faculdade de Ciências, Portugal
2011/07 Skew-product maps and Heterodimensional cycles
(Thesis) Main arguer
 Maria de La Salete Dias Esteves (PhD)
Universidade do Porto Faculdade de Ciências, Portugal
2011/07 Random Walks, Boundary Theory and Hilbert’s Metric
(Thesis) Main arguer
 Gastão Henrique Gonçalves de Bettencourt, (PhD)
Universidade da Beira Interior, Portugal
2011/01 On Random Matrix and its Applications
(Thesis) Main arguer
 Mário Frengue Getimane (PhD)
Universidade do Minho Escola de Medicina, Portugal
2009 Geometry of Hyperbolic Measures and the Liftability Problem
(Thesis) Main arguer
 Carla Lopes Dias (PhD)
Universidade do Porto Faculdade de Ciências, Portugal
2000/03 Uma abordagem functorial à Teoria do Kneading
(Thesis) Main arguer
 João Lui´s Gonçalves Dias Ferreira Alves (PhD)
Universidade de Lisboa Instituto Superior Técnico, Portugal
1998 Global Dynamics for Families of C 2 Endomorphisms in Dimension Greater than One
(Thesis) Main arguer
 Francesc Vilamajó (PhD)
Universitat Autònoma de Barcelona, Spain
1994 Sobre o conjunto minimal de períoodos das aplicações conti´nuas num bouquet de circunferências,
(Thesis) Main arguer
 Ana Maria Alves de Sá (PhD)
Universidade NOVA de Lisboa Faculdade de Ciências e Tecnologia, Portugal

Course / Discipline taught

Academic session Degree Subject (Type) Institution / Organization
2020/01/20 - 2020/01/31 Produtos aleatórios de matrizes, Propriedades estati´sticas Mini-curso (Postgraduate Certificate) Pontifícia Universidade Católica do Rio de Janeiro, Brazil
2017/08 - 2017/08 Continuity of the Lyapunov exponents of linear cocycles Curso avançado, 31º Colóquio Brasileiro de Matemática Instituto Nacional de Matemática Pura e Aplicada, Brazil
Distinctions

Title

2024 Membro correspondente da 1ª Secção (Matemática) da Academia de Ciências de Lisboa