Biography
João Lopes Dias, PhD in Mathematics from the University of Cambridge, currently serves as the Associate Dean of ISEG for the academic affairs. He has held various academic positions, including the head of the Mathematics department at ISEG and the scientific coordination of the CEMAPRE Research Center. He is the author of several scientific publications in the field of dynamical systems and has been active in mentoring postdoctoral researchers and doctoral students.
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 |
|---|---|---|
| 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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| 2023 | New Trends in Lyapunov Exponents Springer International Publishing |
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Proceedings from scholarly meetings
| Year | Title / Publication | Link |
|---|---|---|
| 2023 | Hyperbolicity or Zero Lyapunov Exponents for C2-Hamiltonians 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 Gestão - Gestão, Licenciatura Bolonha em Finanças - Finance, Licenciatura Bolonha em Matemática Aplicada à Economia e à Gestão - Matemática Aplicada à Economia e à Gestão, Licenciatura Bolonha em Finanças - Finanças, Licenciatura Bolonha em Economia - Economia | 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 |