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This paper is about the ergodic theory of attractors and conservative dynamical systems with hyperbolic properties on large parts (though not necessarily all) of their phase spaces. The main results
Recurrence times and rates of mixing
  • L. Young
  • Mathematics, Economics
  • 1 November 1999
The setting of this paper consists of a map making “nice” returns to a reference set. Criteria for the existence of equilibria, speed of convergence to equilibria and for the central limit theorem
The metric entropy of diffeomorphisms
Soit M une variete de Riemann compacte C ∞ sans bord, soit f un diffeomorphisme C 2 de M, et soit m une mesure de probabilite de Borel f-invariante sur M. Soit h m (f) l'entropie de f. On donne des
Dimension, entropy and Lyapunov exponents
  • L. Young
  • Mathematics
    Ergodic Theory and Dynamical Systems
  • 1 March 1982
Abstract We consider diffeomorphisms of surfaces leaving invariant an ergodic Borel probability measure μ. Define HD (μ) to be the infimum of Hausdorff dimension of sets having full μ-measure. We
The metric entropy of diffeomorphisms Part II: Relations between entropy, exponents and dimension
On considere f: (M,m)→(M,m) un C 2 -diffeomorphisme f d'une variete de Riemann compacte M preservant une mesure de probabilite de Borel m. Soit hm(f) l'entropie metrique de f et λ 1 (x)>...>λ r(x)
On the spectra of randomly perturbed expanding maps
We consider small random perturbations of expanding and piecewise expanding maps and prove the robustness of their invariant densities and rates of mixing. We do this by proving the robustness of the
The metric entropy of diffeomorphisms Part I: Characterization of measures satisfying Pesin's entropy formula
Soit M une variete de Riemann compacte, soit f:M→M un diffeomorphisme, et soit m une mesure de probabilite de Borel f-invariante sur M. On identifie les mesures pour lesquelles l'inegalite de
Ergodic Theory of Differentiable Dynamical Systems
These notes are about the dynamics of systems with hyperbolic properties. The setting for the first half consists of a pair (f, µ), where f is a diffeomorphism of a Riemannian manifold and µ is an
Escape rates and conditionally invariant measures
We consider dynamical systems on domains that are not invariant under the dynamics—for example, a system with a hole in the phase space—and raise issues regarding the meaning of escape rates and