Hyperbolic Dynamics, Fluctuations and Large Deviations

Description

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 Center Interfacultaire Bernoulli, Ecole Polytechnique Federale 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 Content: Introduction / Dmitry Dolgopyat, Yakov Pesin, Mark Pollicott and Luchezar Stoyanov -- The almost Borel structure of diffeomorphisms with some hyperbolicity / Jérôme Buzzi -- Lectures on large deviations in probability and dynamical systems / Yuri Kifer -- Thermodynamic formalism for countable Markov shifts / Omri M. Sarig -- Limit theorems for horocycle flows / Giovanni Forni -- Limit theorems in dynamical systems using the spectral method / Sébastien Gouëzel -- Kinetic limits of dynamical systems / Jens Marklof -- Limit theorems for toral translations / Dmitry Dolgopyat and Bassam Fayad -- Spectral gap properties and limit theorems for some random walks and dynamical systems / Yves Guivarc'h -- The martingale approach after Varadhan and Dolgopyat / Jacopo De Simoi and Carlangelo Liverani --