Hyperbolic Dynamics, Fluctuations and Large Deviations

Hyperbolic Dynamics, Fluctuations and Large Deviations

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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.
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Product details

  • Hardback | 337 pages
  • 178 x 254 x 25.4mm | 762.04g
  • Providence, United States
  • English
  • 1470411121
  • 9781470411121
  • 2,757,183

Table of contents

Hyperbolic dynamics, fluctuations and large deviations by D. Dolgopyat, Y. Pesin, M. Pollicott, and L. Stoyanov
Large deviations and thermodynamical formalism: The almost Borel structure of diffeomorphisms with some hyperbolicity by J. Buzzi
Lectures on large deviations in probability and dynamical systems by Y. Kifer
Thermodynamic formalism for countable Markov shifts by O. M. Sarig
Limit theorems for dynamical systems: Limit theorems for horocycle flows by G. Forni
Limit theorems in dynamical systems using the spectral method by S. Gouezel
Kinetic limits of dynamical systems by J. Marklof
Additional topics: Limit theorems for toral translations by D. Dolgopyat and B. Fayad
Spectral gap properties and limit theorems for some random walks and dynamical systems by Y. Guivarc'h
The martingale approach after Varadhan and Dolgopyat by J. De Simoi and C. Liverani
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About Dmitry Dolgopyat

D. Dolgopyat, University of Maryland, College Park, MD, USA.

Y. Pesin, Pennsylvania State University, University Park, PA, USA.

M. Pollicott, University of Warwick, Coventry, United Kingdom.

L. Stoyanov, University of Western Australia, Crawley, Australia.
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