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A Measure Associated with Axiom-A Attractors

David Ruelle
American Journal of Mathematics
Vol. 98, No. 3 (Autumn, 1976), pp. 619-654
DOI: 10.2307/2373810
Stable URL: http://www.jstor.org/stable/2373810
Page Count: 36
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A Measure Associated with Axiom-A Attractors
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Abstract

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

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