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September  2003, 9(5): 1185-1192. doi: 10.3934/dcds.2003.9.1185

Periodic probability measures are dense in the set of invariant measures

Michihiro Hirayama 1,

1. 

Graduate School of Mathematics, Kyushu University, Fukuoka 812-8581, Japan

Received  August 2002 Revised  December 2002 Published  June 2003

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: nonuniformly hyperbolic systems., Shadowing.
Mathematics Subject Classification: 37C50, 37D2.
Citation: Michihiro Hirayama. Periodic probability measures are dense in the set of invariant measures. Discrete & Continuous Dynamical Systems, 2003, 9 (5) : 1185-1192. doi: 10.3934/dcds.2003.9.1185
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