A Measure Associated with Axiom-A Attractors

descriptionPublicationkeyboard_double_arrow_right Article , Part of book or chapter of book 01 Jan 1976Publisher:JSTORJournal:American Journal of Mathematics, volume 98, page 619 (issn: 0002-9327,

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Authors: Ruelle, David;

doi: 10.2307/2373810 , 10.1142/9789812833709_0006

A Measure Associated with Axiom-A Attractors

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Abstract

The future orbits of a diffeomorphism near an Axiom-A attrac- tor are investigated. It is found that their asymptotic behavior is in general described by a fixed probability measure yt carried by the attractor. The measure It has an exponential cluster property, and satisfies a variational principle.

Keywords

Dynamical systems with hyperbolic behavior, Set functions and measures on topological groups or semigroups, Haar measures, invariant measures, Convergence of probability measures

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