Periodic probability measures are dense in the set of invariant measures

Michihiro Hirayama

doi:10.3934/dcds.2003.9.1185

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2003, Volume 9, Issue 5: 1185-1192. Doi: 10.3934/dcds.2003.9.1185

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Periodic probability measures are dense in the set of invariant measures

Michihiro Hirayama^1,

1.
Graduate School of Mathematics, Kyushu University, Fukuoka 812-8581

Received: July 31, 2002

Revised: November 30, 2002

Published: August 2003

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Abstract

We show that if a mixing diffeomorphism of a compact manifold preserves an ergodic hyperbolic probability measure, then the measures supported by hyperbolic periodic points are dense in the set of invariant measures. This is a generalization of the result shown by Sigmund.

Keywords:

Shadowing,
nonuniformly hyperbolic systems.

Mathematics Subject Classification: 37C50, 37D25.

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