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Partially Hyperbolic Dynamics, Laminations, and Teichmüller Flow
Edited by: Giovanni Forni, University of Toronto, ON, Canada, Mikhail Lyubich, State University of New York at Stony Brook, NY, and Charles Pugh and Michael Shub, University of Toronto, ON, Canada
A co-publication of the AMS and Fields Institute.
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Fields Institute Communications
2007; 339 pp; hardcover
Volume: 51
ISBN-10: 0-8218-4274-9
ISBN-13: 978-0-8218-4274-4
List Price: US$112
Member Price: US$89.60
Order Code: FIC/51
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This volume collects a set of contributions by participants of the Workshop "Partially hyperbolic dynamics, laminations, and Teichmüller flow" held at the Fields Institute in Toronto in January 2006. The Workshop brought together several leading experts in two very active fields of contemporary dynamical systems theory: partially hyperbolic dynamics and Teichmüller dynamics. They are unified by ideas coming from the theory of laminations and foliations, dynamical hyperbolicity, and ergodic theory. These are the main themes of the current volume. The volume contains both surveys and research papers on non-uniform and partial hyperbolicity, on dominated splitting and beyond (in Part I), Teichmüller dynamics with applications to interval exchange transformations and on the topology of moduli spaces of quadratic differentials (in Part II), foliations and laminations and other miscellaneous papers (in Part III). Taken together these papers provide a snapshot of the state of the art in some of the most active topics at the crossroads between dynamical systems, smooth ergodic theory, geometry and topology, suitable for advanced graduate students and researchers. Non-specialists will find the extensive, in-depth surveys especially useful.

Titles in this series are co-published with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).

Readership

Graduate students and research mathematicians interested in dynamical systems theory.

Table of Contents

Part I - Partially Hyperbolic Dynamics
  • L. J. Díaz -- How to put a stop to domination once and for all (and what comes afterwards)
  • F. R. Hertz, M. A. R. Hertz, and R. Ures -- A survey of partially hyperbolic dynamics
  • E. R. Pujals -- From hyperbolicity to dominated splitting
  • F. R. Hertz, M. A. R. Hertz, and R. Ures -- Some results on the integrability of the center bundle for partially hyperbolic diffeomorphisms
Part II - Teichmüller Dynamics
  • K. Calta and J. Smillie -- The \(J\)-invariant, exceptional surfaces and notions of periodicity
  • J. Smillie and B. Weiss -- Finiteness results for flat surfaces: A survey and problem list
  • M. Viana -- Lyapunov exponents of Teichmüller flows
  • A. Avila and A. Bufetov -- Exponential decay of correlations for the Rauzy-Veech-Zorich induction map
  • Y. Cheung and A. Eskin -- Unique ergodicity of translation flows
  • H. Masur and A. Zorich -- Combinatorial geometry of generic degenerations of quadratic differentials
Part III-Miscellaneous
  • A. Biś -- Dynamics of foliated spaces in codimension greater than one
  • A. Glutsyuk -- A survey on minimality of horospheric laminations for rational functions
  • Y. Pesin and K. Zhang -- Thermodynamics of inducing schemes and liftability of measures
  • M. Gerber -- Pseudo-Anosov maps and Wojtkowski's cone methods
  • M. Pollicott -- Distribution of orbits for Möbius groups
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