New Trends in Lyapunov Exponents : NTLE, Lisbon, Portugal, February 7-11, 2022 (Cim Series in Mathematical Sciences)

Dias, João Lopes (EDT)/ Duarte, Pedro (EDT)/ Gaivão, José Pedro (EDT)

Springer International Publishing AG（2023/10発売）

• 製本 Hardcover:ハードカバー版／ページ数 179 p.
• 商品コード 9783031413155

Full Description

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.

Contents

Preface.- Lyapunov Exponents for Linear Homogeneous Differential Equations.- An invitation to SL2(R) cocycles over random dynamics.- Randomness Versus Quasi-Periodicity.- Hyperbolicity or Zero Lyapunov Exponents for C2-Hamiltonians.- Generalized Lyapunov exponents and aspects of the theory of deep learning.- On the Multifractal Formalism of Lyapunov Exponents: A Survey of Recent Results.- The Continuity Problem of Lyapunov Exponents.- Some Questions and Remarks on Lyapunov Irregular Behavior for Linear Cocycles.