STATISTICAL PROPERTIES OF DYNAMICAL SYSTEMS WITH SOME HYPERBOLICITY
- L. Young
- Mathematics
- 1 May 1998
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
- F. Ledrappier, L. Young
- Mathematics
- 1 October 1984
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
- MathematicsErgodic 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…
Ergodic Theory of Differentiable Dynamical Systems
- L. Young
- Mathematics
- 1995
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…
What Are SRB Measures, and Which Dynamical Systems Have Them?
- L. Young
- Physics
- 1 December 2002
This is a slightly expanded version of the text of a lecture I gave in a conference at Rutgers University in honor of David Ruelle and Yasha Sinai. In this lecture I reported on some of the main…
Periodic points and topological entropy of one dimensional maps
- Louis Block, J. Guckenheimer, M. Misiurewicz, L. Young
- Mathematics
- 1980
Entropy in dynamical systems
- L. Young
- Computer Science
- 2003
This article will attempt to give a brief survey of the role of entropy in dynamical systems and especially in smooth ergodic theory, namely the relation of entropy to Lyapunov exponents and dimension, which I will discuss in some depth.
The metric entropy of diffeomorphisms Part I: Characterization of measures satisfying Pesin's entropy formula
- F. Ledrappier, L. Young
- Mathematics
- 1 November 1985
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…
The metric entropy of diffeomorphisms Part II: Relations between entropy, exponents and dimension
- F. Ledrappier, L. Young
- Mathematics
- 1 November 1985
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)…
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