Hyperbolic Dynamics, Fluctuations and Large Deviations
About this Title
D. Dolgopyat, University of Maryland, College Park, MD, Y. Pesin, Pennsylvania State University, University Park, PA, M. Pollicott, University of Warwick, Coventry, United Kingdom and L. Stoyanov, University of Western Australia, Crawley, Australia, Editors
Publication: Proceedings of Symposia in Pure Mathematics
Publication Year 2015: Volume 89
ISBNs: 978-1-4704-1112-1 (print); 978-1-4704-2266-0 (online)
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.
Graduate students and research mathematicians interested in dynamical systems, ergodic theory, statistical mechanics, and mathematical physics.
Table of Contents
- Dmitry Dolgopyat, Yakov Pesin, Mark Pollicott and Luchezar Stoyanov – Introduction
- 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
- 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
- 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