Modern Aspects of Dynamical Systems : Cetraro, Italy 2021 / by Manfred Einsiedler, Giovanni Forni, Vadim Kaloshin, Jasmin Raissy ; edited by Claudio Bonanno, Alfonso Sorrentino, Corinna Ulcigrai.

Format:

Book

Contributor:

Bonanno, Claudio, editor.

Series:

C.I.M.E. Foundation Subseries, 2946-1820 ; 2347

Language:

English

Subjects (All):

Dynamics.

Dynamical Systems.

Local Subjects:

Dynamical Systems.

Physical Description:

1 online resource (232 pages)

Edition:

1st ed. 2024.

Place of Publication:

Cham : Springer Nature Switzerland : Imprint: Springer, 2024.

Summary:

This book provides an overview of recent advances in the theory of dynamical systems, with a particular emphasis on their connections to other areas of mathematical research, including number theory, geometry, mathematical physics, complex analysis, and celestial mechanics. Compiling the lecture notes from some of the contributions presented at the C.I.M.E. school "Modern Aspects of Dynamical Systems" held in Cetraro in August 2021, the contributions are the following: “Homogeneous dynamics and Diophantine problems” by Manfred Einsiedler, “Effective ergodic theory for translation flow” by Giovanni Forni, “Integrability and rigidity for convex billiards” by Vadim Kaloshin, “Holomorphic dynamics” by Jasmin Raissy and “Exponentially small phenomena and its role in the dynamics” by Tere Martinez-Seara. These notes are suitable for graduate students and young researchers interested in an introduction to some of the modern research areas within the field of dynamical systems.

Contents:

- Homogeneous Dynamics and its connection to Diophantine Approximation

Effective unique ergodicity and weak mixing of translation flows

Lecture notes on Birkhoff billiards: dynamics, integrability and spectral rigidity

Introduction to Fatou components in holomorphic dynamics.

Notes:

Includes bibliographical references.

ISBN:

3-031-62014-3