Hyperbolic Dynamics, Large Deviations and Fluctuations
1 January - 30 June 2013
Centre Interfacultaire Bernoulli, EPF Lausanne
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About the special programme
During the last 50 years statistical properties of dynamical systems of various types and in many different situations have been a 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 a whole lot of areas in mathematics, physics, engineering and biology. The systematic study of statistical properties of dynamical systems began in the early 60's with the works of Sinai and Ruelle, and later Bowen, who laid the foundations of thermodynamics. Though the methods they developed were of rather general nature, their applications were restricted mostly to uniformly hyperbolic systems due to the limitations of the techniques available at the time. Much wider horizons were opened in the 70's with the works of Pesin who laid the foundations of the ergodic theory of non-uniformly hyperbolic systems. This was followed by an extensive activity in studying and further developing of what is now known as `Pesin's theory', and it facilitated a great deal the study of uniformly hyperbolic systems as well. At present it is widely accepted that uniformly hyperbolic systems are, in general, well understood, although some important problems still remain unsolved. The main activities are in studying non-uniformly hyperbolic systems, hyperbolic systems with singularities, and more generally, systems which posses some kind of hyperbolicity however do not belong to the previously mentioned categories.
The aim of the present program is to bring together leading experts and young researchers working on statistical properties of dynamical systems with some hyperbolicity and their applications in statistical mechanics, thermodynamics, mathematical physics and some other areas.
The Program's topics include, but are not limited to:
- Large deviations and fluctuations for systems with some hyperbolicity
- spectra of transfer operators
- limit theorems in hyperbolic dynamics
- fluctuations for systems with zero entropy
- statistical properties of coupled hyperbolic systems
Schools and and Workshops
A workshop on "Large deviations and thermodynamical formalism" (organized by J. Buzzi (Orsay), S. Luzzatto (Trieste), O. Sarig (Weizmann) and Ya. Pesin (Penn State)) will be held from March 18 to March 22, 2013. The workshop will be preceded by a series of intensive mini-courses for post-graduate and post-doctoral students that will take place from March 11 to March 15, 2013 (with lecturers J. Buzzi (Orsay), Y. Kifer (Jerusalem), O. Sarig (Weizmann)).
A workshop on "Limit Theorems for dynamical systems" (organized by N. Chernov, D. Kleinbock, M. Pollicott and R. Sharp) will be held from June 3 to June 7, 2013. The workshop will be preceded by a series of intensive mini-courses for post-graduate and post-doctoral students that will take place from May 27 till May 31, 2013 (with lecturers G. Forni (Maryland), S. Gouezel (Rennes) and J. Marklof (Bristol).).
Some of the slides for the talks will be available here
There will also be an active visitor and seminar program under which junior and senior researchers will work at EPFL for varying periods.
There will also be individual "Bernoulli lectures" by keynote speakers.
Bernoulli Lectures
There will also be a a number of special lectures by three distinguished speakers
- Y. Pesin (Penn State), Appearance and Genericity of chaos (& March)
- G. Gallavotti (Rome), Hyperbolic systems and fluctuation theorems (16 May) Slides of talk
- D. Ruelle (IHES), Nonequilibrium Statistical Mechanics: From Heat Transport To Hydrodynamic Turbulence (30, May) Slides of talk
Scientific Organizing Committee
Dmitry Dolgopyat (University of Maryland)
Yakov Pesin (Penn State)
Mark Pollicott (Warwick University)
Luchezar Stoyanov (University of Western Australia)
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Dmitry Dolgopyat |
Yakov Pesin |
Mark Pollicott |
Luchezar Stoyanov |
Long term visitors ( > 1 month)
Dmitry Dolgopyat, University of Maryland (June)
Yuri Kifer, The Hebrew University of Jerusalem (March)
Yakov Pesin, Pennsylvania State University (March-April)
Vesselin Petkov, University of Bordeaux I
Mark Pollicott, Warwick University (March-June)
Jorg Schmeling, University of Lund (March)
Samuel Senti, Federal University of Rio de Janeiro (February-June)
Richard Sharp, University of Warwick (June)
Luchezar Stoyanov, University of Western Australia (May)
Masato Tusjii, Kyushu University (April)
Short term visitors
Viviane Baladi, University of Copenhagen
Peter Balint, Budapest University of Technology and Economics
Jerome Buzzi, Ecole Polytechnique
Nikolai Chernov, University of Alabama at Birmingham
Vaughn Climenhaga, University of Houston
Bassam Fayad, Paris VI
Giovanni Forni, University of Maryland
Sebastien Gouezel, Universite de Rennes 1
Boris Hasselblatt, Tufts University
Dmitriy Kleinbock, Brandeis University
Stefano Luzzatto, International Centre for Theoretical Physics
Jens Marklof, University of Bristol
Ian Melbourne, University of Warwick
Krerley Oliveira, Federal University of Alagoas
Juan Rivera-Letelier, PUC-Chile
Omri Sarig, The Weizmann Institute for Science
Daniel Schnellman, Ecole Normale Superieure
Domokos Szasz, Budapest Technical University
Serge Troubetskoy, Aix-Marsaille University
Paulo Varandas, Federal University of Bahia
Ke Zhang, University of Toronto
Michel Zinsmeister, University of Orleans