Book ChapterDOI
SRB measures for partially hyperbolic systems whose central direction is mostly expanding
TLDR
In this article, the authors construct a measure supported on partially hyperbolic sets of diffeomorphisms, where the tangent bundle splits into two invariant subbundles, one of which is uniformly contracting, and the complementary subbundle is non-uniformly expanding.Abstract:
We construct Sinai-Ruelle-Bowen (SRB) measures supported on partially hyperbolic sets of diffeomorphisms — the tangent bundle splits into two invariant subbundles, one of which is uniformly contracting — under the assumption that the complementary subbundle is non-uniformly expanding. If the rate of expansion (Lyapunov exponents) is bounded away from zero, then there are only finitely many SRB measures. Our techniques extend to other situations, including certain maps with singularities or critical points, as well as diffeomorphisms having only a dominated splitting (and no uniformly hyperbolic subbundle).read more
Citations
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Phd by thesis
TL;DR: In this paper, a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) is presented.
Journal ArticleDOI
SRB measures for partially hyperbolic systems whose central direction is mostly expanding
TL;DR: In this article, the authors construct the Sinai-Ruelle-Bowen (SRB) measures supported on partially hyperbolic sets of diffeomorphisms under the assumption that the complementary subbundle is non-uniformly expanding.
Journal ArticleDOI
A C^1-generic dichotomy for diffeomorphisms: Weak forms of hyperbolicity or infinitely many sinks or sources
TL;DR: In this article, it was shown that any Cl-robustly transitive diffeomorphism admits a dominated splitting, which is a generalization of a bidimensional result of Mafine [Ma3].
Book
Lectures on Lyapunov Exponents
TL;DR: In this article, the authors introduce linear cocycles, Extremal Lyapunov exponents and invariant measures, as well as a generic cocycle based on the invariance principle.
References
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Journal ArticleDOI
Deterministic nonperiodic flow
TL;DR: In this paper, it was shown that nonperiodic solutions are ordinarily unstable with respect to small modifications, so that slightly differing initial states can evolve into considerably different states, and systems with bounded solutions are shown to possess bounded numerical solutions.
Book
Random Perturbations of Dynamical Systems
M. I. Freĭdlin,A. D. Ventt︠s︡elʹ +1 more
TL;DR: In this article, the authors introduce the concept of random perturbations in Dynamical Systems with a Finite Time Interval (FTI) and the Averaging Principle.
Book ChapterDOI
Differentiable dynamical systems
TL;DR: A survey article on the area of global analysis defined by differentiable dynamical systems or equivalently the action (differentiable) of a Lie group G on a manifold M is presented in this paper.
BookDOI
Equilibrium states and the ergodic theory of Anosov diffeomorphisms
TL;DR: Gibbs Measures and Gibbs measures have been used in this article to define Axiom a Diffeomorphisms for general Thermodynamic Formalism and Ergodic Theory of Axiom-a-Diffeomorphism.
Journal ArticleDOI
On the nature of turbulence
David Ruelle,Floris Takens +1 more
TL;DR: A mechanism for the generation of turbulence and related phenomena in dissipative systems is proposed in this article, where the authors propose a mechanism for generating turbulence in a dissipative system with respect to dissipative energy.