Biography
João Lopes Dias, doutorado em Matemática pela Universidade de Cambridge, é atualmente vice-presidente do ISEG com o pelouro dos assuntos académicos. Ocupou vários cargos académicos, incluindo a presidência do departamento de Matemática do ISEG e a coordenação científica do centro de Investigação CEMAPRE. É autor de diversas publicações científicas na área de sistemas dinâmicos e tem sido ativo na orientação de investigadores de pós-doutoramento e de estudantes de doutoramento.
Education
| 2011 | Agregação, Matemática Aplicada à Economia e Gestão ISEG, Universidade Técnica de Lisboa (Portugal) |
| 2002 | PhD in Mathematics University of Cambridge (United Kingdom) |
| 1996 | Licenciado em Engª Fisica Tecnológica Instituto Superior Técnico (Portugal) |
Publications & Citations
Journal article
| Year | Title / Publication | Link |
|---|---|---|
| 2024 | Billiards in generic convex bodies have positive topological entropy Advances in Mathematics |
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| 2021 | Hyperbolic polygonal billiards close to 1-dimensional piecewise expanding maps JOURNAL OF STATISTICAL PHYSICS |
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| 2021 | Expansiveness and Hyperbolicity in Convex Billiards REGULAR AND CHAOTIC DYNAMICS |
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| 2020 | The attractor of piecewise expanding maps of the interval Stochastics and Dynamics |
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| 2020 | Hyperbolicity through stable shadowing for generic geodesic flows Physica D: Nonlinear Phenomena |
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| 2020 | Reducibility of quasi-periodically forced circle flows Discrete and Continuous Dynamical Systems - Series A |
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| 2019 | Linearization of Gevrey flows on Td with a Brjuno type arithmetical condition Journal of Differential Equations |
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| 2018 | Hyperbolic polygonal billiards with finitely many ergodic SRB measures Cambridge University Press |
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| 2017 | On shadowing and hyperbolicity for geodesic flows on surfaces Nonlinear Analysis - Real World Applications |
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| 2016 | Hyperbolic polygonal billiards with finitely many ergodic SRB measures Ergodic Theory and Dynamical Systems |
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| 2014 | Realization of tangent perturbations in discrete and continuous time conservative systems Discrete and Continuous Dynamical Systems |
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| 2014 | Hamiltonian suspension of perturbed Poincaré sections and an application Mathematical Proceedings of the Cambridge Philosophical Society |
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| 2014 | SRB measures for polygonal billiards with contracting reflection laws Communications in Mathematical Physics |
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| 2014 | Ergodicity of polygonal slap maps Nonlinearity |
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| 2011 | On the Herman-Avila-Bochi formula for Lyapunov exponents of SL(2,R)-cocycles Nonlinearity |
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| 2009 | Hamiltonian Elliptic Dynamics on Symplectic 4-Manifolds Proceedings of the American Mathematical Society |
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| 2008 | Local conjugacy classes for analytic torus flows Journal of Differential Equations |
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| 2008 | Generic Dynamics of 4 Dimensional C2 Hamiltonian Systems Communications in Mathematical Physics |
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| 2008 | Renormalization of diophantine skew flows, with applications to the reducibility problem Discrete and Continuous Dynamical Systems - Series A |
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| 2007 | Multidimensional continued fractions, dynamic renormalization and KAM theory Communications in Mathematical Physics |
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| 2006 | A normal form theorem for Brjuno skew systems through renormalization Journal of Differential Equations |
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| 2006 | Brjuno condition and renormalization for Poincaré flows Discrete and Continuous Dynamical Systems - Series A |
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| 2006 | Renormalization for multidimensional Hamiltonian flows Nonlinearity |
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| 2002 | Renormalization of flows on the multidimensional torus close to a KT frequency vector Nonlinearity |
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| 2002 | Renormalization scheme for vector fields on T2 with a diophantine frequency Nonlinearity |
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Chapter
| Year | Title / Publication | Link |
|---|---|---|
| 2023 | Hyperbolicity or Zero Lyapunov Exponents for C2-Hamiltonians Springer, CIM Series in Mathematical Sciences |
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| 2016 | Polygonal billiards with strongly contractive reflection laws: a review of some hyperbolic properties Difference Equations, Discrete Dynamical Systems and Applications, Eds. L. Alseda i Soler et al., Springer Proceedings in Mathematics and Statistics 180 |
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| 2014 | From ice to penguins: the role of mathematics in Antarctic research Springer, CIM Series in Mathematical Sciences |
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| 2014 | Review on non-perturbative reducibility of quasi-periodically forced linear flows with two frequencies Springer, CIM Series in Mathematical Sciences |
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| 2011 | Generic Hamiltonian Dynamical Systems: An Overview. Springer |
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| 2011 | KAM Theory as a Limit of Renormalization Springer |
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Book
| Year | Title / Publication | Link |
|---|---|---|
| 2015 | Introdução à integração em Rn Almedina |
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Book editor
| Year | Title / Publication | Link |
|---|---|---|
| 2023 | International Workshop New Trends in Lyapunov Exponents Springer, CIM Series in Mathematical Sciences |
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Teaching
2022/2023
| Semester | Course | Degree | Coordinator |
|---|---|---|---|
| 2º | Análise Complexa e Equações Diferenciais | Licenciatura Bolonha em Finanças - Finanças, Licenciatura Bolonha em Matemática Aplicada à Economia e à Gestão - Matemática Aplicada à Economia e à Gestão, Licenciatura Bolonha em Economia - Economia, Licenciatura Bolonha em Gestão - Gestão, Licenciatura Bolonha em Finanças - Finance | Yes |
| Year | Student Name / Title / Institution | Supervision Type | Link |
|---|---|---|---|
| 2022/2023 | MARTIM ROBERTO ALVES DA COSTA Random product of iid 2 x 2 matrices and a theorem by Furstenberg |
Master | Ver |
| 2018/2019 | DANIEL TOMÁS VITAL DE ALCÂNTARA Berry-Esseen theorem |
Master | Ver |
| 2016/2017 | MAFALDA OLIVEIRA MARTINS BASTOS DE ALMEIDA The Lotka-Volterra equations in Finance and Economics |
Master | Ver |
| 2012/2013 | SARA BÁRBARA DUTRA LOPES Teorema do mergulho de Takens: Reconstrução do espaço de fases de um sistema dinâmico usando séries temporais |
Master | Ver |
| 2012/2013 | NUNO RICARDO MOURA FONTES Sistemas dinâmicos, análise numérica de séries temporais e aplicações às Finanças |
Master | Ver |
| 2011/2012 | FILIPE ANDRÉ PAULINO SANTOS Análise da difusão através de métodos probabilísticos e dimensão de Hausdorff |
Master | Ver |
Professional Experience
| Name / Description | Date | Organization |
|---|---|---|
| Vice-Dean |
2022 | ISEG |
| Presidente de departamento, Matemática Presidente de departamento |
2020 - 2021 | ISEG |
| Coordenador de curso, Matemática Coordenador de curso |
2017 - 2018 | ISEG |
| Membro da coordenação de curso Doutoramento MAEG, Matemática Membro da coordenação de curso |
2016 - 2018 | ISEG |
| Presidente de unidade de investigação, CEMAPRE Presidente de unidade de investigação |
2015 - 2017 | ISEG |
| Membro conselho científico Membro conselho científico |
2015 - 2016 |