[图书][B] Dynamics beyond uniform hyperbolicity: A global geometric and probabilistic perspective
In broad terms, the goal of dynamics is to describe the long-term evolution of systems for
which an" infinitesimal" evolution rule, such as a differential equation or the iteration of a …
which an" infinitesimal" evolution rule, such as a differential equation or the iteration of a …
[图书][B] Lectures on partial hyperbolicity and stable ergodicity
YB Pesin - 2004 - books.google.com
This book is an introduction to the modern theory of partial hyperbolicity with applications to
stable ergodicity theory of smooth dynamical systems. It provides a systematic treatment of …
stable ergodicity theory of smooth dynamical systems. It provides a systematic treatment of …
Limit theorems for partially hyperbolic systems
D Dolgopyat - Transactions of the American Mathematical Society, 2004 - ams.org
We consider a large class of partially hyperbolic systems containing, among others, affine
maps, frame flows on negatively curved manifolds, and mostly contracting diffeomorphisms …
maps, frame flows on negatively curved manifolds, and mostly contracting diffeomorphisms …
On differentiability of SRB states for partially hyperbolic systems
D Dolgopyat - Inventiones mathematicae, 2004 - Springer
Consider a one parameter family of diffeomorphisms f ε such that f 0 is an Anosov element in
a standard abelian Anosov action having sufficiently strong mixing properties. Let ν ε be any …
a standard abelian Anosov action having sufficiently strong mixing properties. Let ν ε be any …
[PDF][PDF] Pathological foliations and removable zero exponents
M Shub, A Wilkinson - Inventiones mathematicae, 2000 - math.uchicago.edu
The ergodic theory of uniformly hyperbolic, or “Axiom A”, diffeomorphisms has been studied
extensively, beginning with the pioneering work of Anosov, Sinai, Ruelle and Bowen …
extensively, beginning with the pioneering work of Anosov, Sinai, Ruelle and Bowen …
Accessibility and stable ergodicity for partially hyperbolic diffeomorphisms with 1D-center bundle
F Rodriguez-Hertz, M Rodriguez-Hertz… - arXiv preprint math …, 2006 - arxiv.org
We prove that stable ergodicity is C r open and dense among conservative partially
hyperbolic diffeomorphisms with one-dimensional center bundle, for all r in [2, infty]. The …
hyperbolic diffeomorphisms with one-dimensional center bundle, for all r in [2, infty]. The …
On mixing properties of compact group extensions of hyperbolic systems
D Dolgopyat - Israel journal of mathematics, 2002 - Springer
We study compact group extensions of hyperbolic diffeomorphisms. We relate mixing
properties of such extensions with accessibility properties of their stable and unstable …
properties of such extensions with accessibility properties of their stable and unstable …
Stable ergodicity and julienne quasi-conformality
C Pugh, M Shub - Journal of the European Mathematical Society, 2000 - ems.press
In this paper we dramatically expand the domain of known stably ergodic, partially
hyperbolic dynamical systems. For example, all partially hyperbolic affine diffeomorphisms …
hyperbolic dynamical systems. For example, all partially hyperbolic affine diffeomorphisms …
[PDF][PDF] On dynamics of mostly contracting diffeomorphisms
D Dolgopyat - Communications in Mathematical Physics, 2000 - Citeseer
ON DYNAMICS OF MOSTLY CONTRACTING DIFFEOMORPHISMS. 1. Introduction. This
paper treats a class of partially hyperbolic systems wi Page 1 ON DYNAMICS OF MOSTLY …
paper treats a class of partially hyperbolic systems wi Page 1 ON DYNAMICS OF MOSTLY …
Conformal hamiltonian systems
R McLachlan, M Perlmutter - Journal of Geometry and Physics, 2001 - Elsevier
Vector fields whose flow preserves a symplectic form up to a constant, such as simple
mechanical systems with friction, are called “conformal”. We develop a reduction theory for …
mechanical systems with friction, are called “conformal”. We develop a reduction theory for …