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Asymptotic Counting in Conformal Dynamical Systems
  • Language: en
  • Pages: 139

Asymptotic Counting in Conformal Dynamical Systems

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Dynamical Systems and Ergodic Theory
  • Language: en
  • Pages: 198

Dynamical Systems and Ergodic Theory

This book is an essentially self contained introduction to topological dynamics and ergodic theory. It is divided into a number of relatively short chapters with the intention that each may be used as a component of a lecture course tailored to the particular audience. Parts of the book are suitable for a final year undergraduate course or for a masters level course. A number of applications are given, principally to number theory and arithmetic progressions (through van der waerden's theorem and szemerdi's theorem).

Ergodic Theory and Zd Actions
  • Language: en
  • Pages: 496

Ergodic Theory and Zd Actions

A mixture of surveys and original articles that span the theory of Zd actions.

Thermodynamic Formalism
  • Language: en
  • Pages: 536

Thermodynamic Formalism

This volume arose from a semester at CIRM-Luminy on “Thermodynamic Formalism: Applications to Probability, Geometry and Fractals” which brought together leading experts in the area to discuss topical problems and recent progress. It includes a number of surveys intended to make the field more accessible to younger mathematicians and scientists wishing to learn more about the area. Thermodynamic formalism has been a powerful tool in ergodic theory and dynamical system and its applications to other topics, particularly Riemannian geometry (especially in negative curvature), statistical properties of dynamical systems and fractal geometry. This work will be of value both to graduate students and more senior researchers interested in either learning about the main ideas and themes in thermodynamic formalism, and research themes which are at forefront of research in this area.

Lectures on Ergodic Theory and Pesin Theory on Compact Manifolds
  • Language: en
  • Pages: 176

Lectures on Ergodic Theory and Pesin Theory on Compact Manifolds

These lecture notes provide a unique introduction to Pesin theory and its applications.

Hyperbolic Dynamics, Fluctuations and Large Deviations
  • Language: en
  • Pages: 354

Hyperbolic Dynamics, Fluctuations and Large Deviations

This volume contains the proceedings of the semester-long special program on Hyperbolic Dynamics, Large Deviations and Fluctuations, which was held from January-June 2013, at the Centre Interfacultaire Bernoulli, École Polytechnique Fédérale de Lausanne, Switzerland. The broad theme of the program was the long-term behavior of dynamical systems and their statistical behavior. During the last 50 years, the statistical properties of dynamical systems of many different types have been the subject of extensive study in statistical mechanics and thermodynamics, ergodic and probability theories, and some areas of mathematical physics. The results of this study have had a profound effect on many different areas in mathematics, physics, engineering and biology. The papers in this volume cover topics in large deviations and thermodynamics formalism and limit theorems for dynamic systems. The material presented is primarily directed at researchers and graduate students in the very broad area of dynamical systems and ergodic theory, but will also be of interest to researchers in related areas such as statistical physics, spectral theory and some aspects of number theory and geometry.

Spectral Analysis in Geometry and Number Theory
  • Language: en
  • Pages: 363

Spectral Analysis in Geometry and Number Theory

This volume is an outgrowth of an international conference in honor of Toshikazu Sunada on the occasion of his sixtieth birthday. The conference took place at Nagoya University, Japan, in 2007. Sunada's research covers a wide spectrum of spectral analysis, including interactions among geometry, number theory, dynamical systems, probability theory and mathematical physics. Readers will find papers on trace formulae, isospectral problems, zeta functions, quantum ergodicity, random waves, discrete geometric analysis, value distribution, and semiclassical analysis. This volume also contains an article that presents an overview of Sunada's work in mathematics up to the age of sixty.

Geometric and Probabilistic Structures in Dynamics
  • Language: en
  • Pages: 358

Geometric and Probabilistic Structures in Dynamics

"This book presents a collection of articles that cover areas of mathematics related to dynamical systems. The authors are well-known experts who use geometric and probabilistic methods to study interesting problems in the theory of dynamical systems and its applications. Some of the articles are surveys while others are original contributions. The topics covered include: Riemannian geometry, models in mathematical physics and mathematical biology, symbolic dynamics, random and stochastic dynamics. This book can be used by graduate students and researchers in dynamical systems and its applications."--BOOK JACKET.

Open Conformal Systems and Perturbations of Transfer Operators
  • Language: en
  • Pages: 204

Open Conformal Systems and Perturbations of Transfer Operators

  • Type: Book
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  • Published: 2018-02-05
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  • Publisher: Springer

The focus of this book is on open conformal dynamical systems corresponding to the escape of a point through an open Euclidean ball. The ultimate goal is to understand the asymptotic behavior of the escape rate as the radius of the ball tends to zero. In the case of hyperbolic conformal systems this has been addressed by various authors. The conformal maps considered in this book are far more general, and the analysis correspondingly more involved. The asymptotic existence of escape rates is proved and they are calculated in the context of (finite or infinite) countable alphabets, uniformly contracting conformal graph-directed Markov systems, and in particular, conformal countable alphabet i...

Modern Dynamical Systems and Applications
  • Language: en
  • Pages: 490

Modern Dynamical Systems and Applications

This volume presents a broad collection of current research by leading experts in the theory of dynamical systems.