Metric entropy and the number of periodic points

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Published 27 May 2010 • 2010 IOP Publishing Ltd & London Mathematical Society
, , Citation Gang Liao et al 2010 Nonlinearity 23 1547 DOI 10.1088/0951-7715/23/7/002

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1 School of Mathematical Sciences, Peking University, Beijing 100871, China

2 LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China

3 Author to whom any correspondence should be addressed.

Dates

  1. Received 10 September 2009
  2. Published

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0951-7715/23/7/1547

Abstract

For an ergodic hyperbolic measure μ preserved by a C1+r(r > 0) diffeomorphism f, the exponential growth rate of the number of such periodic points that their atomic measures approximate μ and their Lyapunov exponents approximate the Lyapunov exponents of μ equals the metric entropy hμ(f) (see theorem 2.3). Moreover, this equality holds pointwise μ-a.e. (see theorem 2.4).

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10.1088/0951-7715/23/7/002