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New Trends in Lyapunov Exponents

NTLE, Lisbon, Portugal, February 7–11, 2022

  • Conference proceedings
  • © 2023

Overview

Editors:
  1. João Lopes Dias

    1. Department of Mathematics, CEMAPRE/REM/ISEG, University of Lisbon, Lisbon, Portugal

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  2. Pedro Duarte

    1. Department of Mathematics and CMAFcIO, Faculty of Sciences, University of Lisbon, Lisbon, Portugal

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  3. José Pedro Gaivão

    1. Department of Mathematics, CEMAPRE/REM/ISEG, University of Lisbon, Lisbon, Portugal

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  4. Silvius Klein

    1. Department of Mathematics, Pontifical Catholic University of Rio de Janeiro, Rio de Janeiro, Brazil

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  5. Telmo Peixe

    1. Department of Mathematics, CEMAPRE/REM/ISEG, University of Lisbon, Lisbon, Portugal

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  6. Jaqueline Siqueira

    1. Institute of Mathematics, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil

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  7. Maria Joana Torres

    1. CMAT and Department of Mathematics, University of Minho, Braga, Portugal

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  • Features recent developments in the study of Lyapunov exponents in dynamical systems
  • Explores applications to other areas such as mathematical physics
  • Gathers peer-reviewed surveys by leading experts in the field

Part of the book series: CIM Series in Mathematical Sciences (CIMSMS)

Included in the following conference series:

Conference proceedings info: NTLE 2022.

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Table of contents (8 papers)

  1. Front Matter

    Pages i-vii
    Download chapter PDF

  2. Lyapunov Exponents for Linear Homogeneous Differential Equations

    • Mário Bessa
    Pages 1-18

  3. An Invitation to \(SL_2(\mathbb {R})\) Cocycles Over Random Dynamics

    • Jamerson Bezerra, Mauricio Poletti
    Pages 19-75

  4. Randomness Versus Quasi-Periodicity

    • Ao Cai
    Pages 77-92

  5. Hyperbolicity or Zero Lyapunov Exponents for \(C^2\)-Hamiltonians

    • João Lopes Dias, Filipe Santos
    Pages 93-98

  6. Generalized Lyapunov Exponents and Aspects of the Theory of Deep Learning

    • Anders Karlsson
    Pages 99-118

  7. On the Multifractal Formalism of Lyapunov Exponents: A Survey of Recent Results

    • Reza Mohammadpour
    Pages 119-139

  8. The Continuity Problem of Lyapunov Exponents

    • Adriana Sánchez
    Pages 141-159

  9. Some Questions and Remarks on Lyapunov Irregular Behavior for Linear Cocycles

    • Paulo Varandas
    Pages 161-179
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  1. New Trends in Lyapunov Exponents

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About this book

This volume presents peer-reviewed surveys on new developments in the study of Lyapunov exponents in dynamical systems and its applications to other areas, such as mathematical physics.

Written by leading experts in their fields, the contributions are based upon the presentations given by invited speakers at the “New Trends in Lyapunov Exponents” workshop held in Lisbon, Portugal, February 7–11, 2022. The works focus on the concept of Lyapunov exponents in their various manifestations in dynamical systems along with their applications to mathematical physics and other areas of mathematics. The papers reflect the spirit of the conference of promoting new connections among different subjects in dynamical systems.

This volume aims primarily at researchers and graduate students working in dynamical systems and related fields, serving as an introduction to active fields of research and as a review of recent results as well.



Editors and Affiliations

  • Department of Mathematics, CEMAPRE/REM/ISEG, University of Lisbon, Lisbon, Portugal

    João Lopes Dias, José Pedro Gaivão, Telmo Peixe

  • Department of Mathematics and CMAFcIO, Faculty of Sciences, University of Lisbon, Lisbon, Portugal

    Pedro Duarte

  • Department of Mathematics, Pontifical Catholic University of Rio de Janeiro, Rio de Janeiro, Brazil

    Silvius Klein

  • Institute of Mathematics, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil

    Jaqueline Siqueira

  • CMAT and Department of Mathematics, University of Minho, Braga, Portugal

    Maria Joana Torres

About the editors

João Lopes Dias is an Associate Professor at ISEG - Universidade de Lisboa, Portugal. He did his PhD at the University of Cambridge, UK (2002) in the area of Hamiltonian dynamics and renormalization. His current research interests include topics on quasiperiodic motion, KAM theory, generic properties of dynamical systems and Lyapunov exponents.

Pedro Miguel Duarte is an Associate Professor at Faculdade de Ciências -  Universidade de Lisboa, Portugal. He did his PhD at the  Institute of Pure and Applied Mathematics - IMPA, Brazil (1993). He does research on dynamical systems and ergodic theory, focusing on symplectic and conservative dynamics, random dynamical systems, billiards, evolutionary game dynamics  and linear cocycles.

José Pedro Gaivão is an Assistant Professor at ISEG -  Universidade de Lisboa, Portugal. He did his PhD at the University of Warwick, UK (2010). He does research on dynamical systems and ergodic theory, focusing on symplectic and conservative dynamics, random dynamical systems and billiards.

Silvius Klein is an Assistant Professor at the Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Brazil. He completed his PhD at the University of California, Los Angeles (UCLA) in 2005. He does research at the interface between dynamical systems and mathematical physics, focusing on statistical properties of linear cocycles and localization of discrete, ergodic Schrödinger operators. 

Telmo Peixe is an Assistant Professor at ISEG - Universidade de Lisboa, Portugal. He did his PhD at the Universidade de Lisboa (2015), after getting a Master's degree from the same university. He does research on dynamical systems, focusing on differential equations and evolutionary game theory.

Jaqueline Siqueira is an Assistant Professor at the Universidade Federal do Rio de Janeiro, Brazil. She did her PhD at the Universidade FederalFluminense, Brazil (2013). Her research area is dynamical systems with an emphasis on ergodic theory and, more particularly, on thermodynamic formalism.

Maria Joana Torres is an Assistant Professor at Escola de Ciências - Universidade do Minho, Braga, Portugal. She did her PhD at the Universidade de Lisboa, Portugal (2004), after getting a Master's degree from the Universidade do Porto, Portugal. She does research on dynamical systems, focusing on symplectic and conservative dynamics, random dynamical systems, generic properties of dynamical systems and Lyapunov exponents.


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