Unstable entropy in smooth ergodic theory

Abstract

In this survey we recall basic notions of disintegration of measures and entropy along unstable laminations. We review some roles of unstable entropy in smooth ergodic theory including the so-called invariance principle, Margulis construction of measures of maximal entropy, physical measures and rigidity. We also give some new examples and pose some open questions.

41 pages. Invited paper (Nonlinearity)

References in corpus (5)

• Smoothness of stable holonomies inside center-stable manifolds and the $C^2$ hypothesis in Pugh-Shub and Ledrappier-Young theory
• Maximal entropy measures of diffeomorphisms of circle fiber bundles
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• Partially hyperbolic diffeomorphisms homotopic to the identity on 3-manifolds
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Cited by in corpus (1)

• On the continuity of topological entropy of certain partially hyperbolic diffeomorphisms