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Book DetailsProceedings of Symposia in Pure MathematicsVolume: 89; 2015; 339 ppMSC: Primary 37; 60;
This volume contains the proceedings of the semesterlong 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 longterm 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.ReadershipGraduate students and research mathematicians interested in dynamical systems, ergodic theory, statistical mechanics, and mathematical physics.

Table of Contents

Articles

Dmitry Dolgopyat, Yakov Pesin, Mark Pollicott and Luchezar Stoyanov  Introduction

Large deviations and thermodynamical formalism

Jérôme Buzzi  The almost Borel structure of diffeomorphisms with some hyperbolicity

Yuri Kifer  Lectures on large deviations in probability and dynamical systems

Omri M. Sarig  Thermodynamic formalism for countable Markov shifts

Limit theorems for dynamical systems

Giovanni Forni  Limit theorems for horocycle flows

Sébastien Gouëzel  Limit theorems in dynamical systems using the spectral method

Jens Marklof  Kinetic limits of dynamical systems

Additional topics

Dmitry Dolgopyat and Bassam Fayad  Limit theorems for toral translations

Yves Guivarc’h  Spectral gap properties and limit theorems for some random walks and dynamical systems

Jacopo De Simoi and Carlangelo Liverani  The martingale approach after Varadhan and Dolgopyat


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This volume contains the proceedings of the semesterlong 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 longterm 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.
Graduate students and research mathematicians interested in dynamical systems, ergodic theory, statistical mechanics, and mathematical physics.

Articles

Dmitry Dolgopyat, Yakov Pesin, Mark Pollicott and Luchezar Stoyanov  Introduction

Large deviations and thermodynamical formalism

Jérôme Buzzi  The almost Borel structure of diffeomorphisms with some hyperbolicity

Yuri Kifer  Lectures on large deviations in probability and dynamical systems

Omri M. Sarig  Thermodynamic formalism for countable Markov shifts

Limit theorems for dynamical systems

Giovanni Forni  Limit theorems for horocycle flows

Sébastien Gouëzel  Limit theorems in dynamical systems using the spectral method

Jens Marklof  Kinetic limits of dynamical systems

Additional topics

Dmitry Dolgopyat and Bassam Fayad  Limit theorems for toral translations

Yves Guivarc’h  Spectral gap properties and limit theorems for some random walks and dynamical systems

Jacopo De Simoi and Carlangelo Liverani  The martingale approach after Varadhan and Dolgopyat