# Mathematical Sciences Research Institute

Home » Clay Mathematics Institute and MSRI Conference on Recent Progress in Dynamics

# Workshop

Clay Mathematics Institute and MSRI Conference on Recent Progress in Dynamics September 27, 2004 - October 01, 2004
 Registration Deadline: October 01, 2004 about 10 years ago June 27, 2004 over 10 years ago
Organizers Michael Brin, Boris Hasselblatt (chair), Gregory Margulis, Yakov Pesin, Peter Sarnak, Klaus Schmidt, Ralf Spatzier, Robert Zimmer
Speaker(s)

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Description

The scope of the conference will be fairly wide, but it will emphasize specific problems in dynamical systems, smooth ergodic theory, and related topics, including differential geometry, group theory and number theory, to name a few, that have seen much progress, but where significant problems vital to the field remain open. Specific examples are the Katok entropy rigidity conjecture for geodesic flows of negatively curved manifolds, the Boltzmann ergodic hypothesis, Liouvillean phenomena, the construction of metrics with ergodic geodesic flow, smooth rigidity of actions of abelian groups of higher rank. This workshop will include a session to discuss open problems and to produce a list of these, with the intent of producing a concrete agenda for further research on several fronts. The following are some of the subjects related to dynamical systems that have seen outstanding advances recently, and that will be significant components of this workshop.

• Billiards, and the question of their hyperbolicity and ergodicity.
• The theory of partially hyperbolic systems and nonuniformly hyperbolic systems.
• The close relations between dynamical systems and differential (especially Riemannian) geometry.
• The significant interactions that have developed between dynamical systems and number theory.
• The extension of methods from the study of invariant measures for homogeneous and affine actions of higher rank abelian groups, initiated by Furstenberg's x2,x3-question, to other areas.
• The study of actions of lattices in semisimple Lie groups.
• The impact on statistical physics of Ruelle's work showing that a generalized Sinai--Ruelle--Bowen-state depends differentiably on the hyperbolic diffeomorphism for which it is defined.

The workshop will be held on the occasion of the 60th birthday of Anatole Katok. We will take this occasion to honor Katok during the conference for his significant influence on almost all areas in dynamical systems through his research, collaboration, teaching, organization and exposition. This workshop is sponsored by the Clay Mathematical Institute and hosted by MSRI. It also benefits from generous contributions from Tufts University and the Pennsylvania State University.

Funding & Logistics

## Show Funding

To apply for funding, you must register by the funding application deadline displayed above.

Students, recent Ph.D.'s, women, and members of underrepresented minorities are particularly encouraged to apply. Funding awards are typically made 6 weeks before the workshop begins. Requests received after the funding deadline are considered only if additional funds become available.

## Show Lodging

MSRI has preferred rates at the Rose Garden Inn, depending on room availability. Reservations may be made by calling 1-800-992-9005 OR directly on their website. Click on Corporate at the bottom of the screen and when prompted enter code MATH (this code is not case sensitive). By using this code a new calendar will appear and will show the MSRI rate on all room types available.

MSRI has preferred rates at the Hotel Durant. Reservations may be made by calling 1-800-238-7268. When making reservations, guests must request the MSRI preferred rate. If you are making your reservations on line, please go to this link and enter the promo/corporate code 123MSRI. Our preferred rate is $139 per night for a Deluxe Queen/King, based on availability. MSRI has preferred rates of$149 - $189 plus tax at the Hotel Shattuck Plaza, depending on room availability. Guests can either call the hotel's main line at 510-845-7300 and ask for the MSRI- Mathematical Science Research Inst. discount; or go to www.hotelshattuckplaza.com and click Book Now. Once on the reservation page, click “Promo/Corporate Code“ and input the code: msri. MSRI has preferred rates of$110 - \$140 at the Berkeley Lab Guest House, depending on room availability. Reservations may be made by calling 510-495-8000 or directly on their website. Select “I am an individual traveler affiliated with MSRI”.

Additional lodging options may be found on our short term housing page.

## Show Visa/Immigration

Schedule
Sep 27, 2004
Monday
 09:30 AM - 10:30 AM Hyperbolic Dynamics and Riemannian Geometry. Gerhard Knieper 01:35 PM - 02:20 PM Symbolic Extension and Entropy Structure. Mike Boyle 02:30 PM - 03:15 PM Long time Asymptotics in Averaging. Dmitry Dolgopyat 04:15 PM - 05:15 PM Five Most Resistant Problems in Dynamics. Anatole Katok (Pennsylvania State University)
Sep 28, 2004
Tuesday
 09:00 AM - 09:45 AM Rigidity , KAM and other Methods. Danijela Damjanovic 11:15 AM - 12:00 AM Local Rigidity: Past, Present, Future. David Fisher (Indiana University) 01:45 PM - 02:30 PM Parameter Exclusion and Markov Structure for Henon-like Families. Michael Jakobson 02:40 PM - 03:35 PM Measure Rigidity of Higher Rank Actions. Manfred Einsiedler (Eidgenössische TH Zürich-Hönggerberg) 04:00 PM - 04:45 PM Averaging Revisited. Yuri Kifer
Sep 29, 2004
Wednesday
 09:55 AM - 10:40 AM Horocycle Flow on Periodic Surfaces. François Ledrappier (University of Notre Dame) 11:15 AM - 12:00 AM The Zorich-Kontsevich Conjecture. Marcelo Viana 01:45 PM - 02:45 PM On Area Preserving Disc Diffeomorphisms. Bassam Fayad 02:50 PM - 03:15 PM The Lorenz Attractor is Mixing. Stefano Luzzatto 03:15 PM - 03:45 PM Statistical Limit Theorems for Suspension Flow. Andrew Torok 04:00 PM - 04:20 PM Stability of Mixing and Rapid Mixing for Axiom A Flows. Michael Field 04:30 PM - 04:55 PM Unique Ergodicity for Non-Uniquely Ergodic Systems. Omri Sarig 05:00 PM - 05:40 PM Stable Ergodicity. Keith Burns 05:45 PM - 06:00 PM Equilibriums of Some Non-Holder Potentials. Huyi Hu
Sep 30, 2004
Thursday
 09:00 AM - 09:45 AM Isomorphism Rigidity. Karl Schmidt 09:50 AM - 10:35 AM Classifying Anosov Diffeomorphisms. Ralf Spatzier (University of Michigan) 11:00 AM - 11:45 AM Rigidity of Compact Foliations. Steven Hurder 01:15 PM - 02:00 PM Understanding Genomes Using Dynamical Systems. James Yorke 02:15 PM - 03:00 PM Some Applications of Hitting Time Asymptotics -from Circle Covers to Dyadic Approximation. Joerg Schmeling 04:15 PM - 05:00 PM Facts and Problems in a more Quantitative Symplectic Geometry. Helmut Hofer (Institute for Advanced Study)
Oct 01, 2004
Friday
 09:00 AM - 09:45 AM Markov Approximations and Stochastic Properties of Billiards. Domokos Szasz 09:50 AM - 10:35 AM Quasi Simplicity and Disjointness. Jean-Paul Thouvenot 11:15 AM - 12:00 PM Flat Surfaces. Anton Zorich (L'Institut de Mathématiques de Jussieu) 02:00 PM - 02:45 PM Self-Similiar Sets in the Plane with Positive Measure. Mark Pollicott (University of Warwick) 02:50 PM - 03:35 PM Ergodic Natural Measures. Michal Misiurewicz 04:10 PM - 05:00 PM Symbolic Extensions and Smooth System Sheldon Newhouse