The Metric Entropy of Endomorphisms

被引：14

作者：

Shu, Lin ^{[1
]}

机构：

[1] Peking Univ, Sch Math Sci, LMAM, Beijing 100871, Peoples R China

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2009年 / 291卷 / 02期

关键词：

NEGATIVE LYAPUNOV EXPONENTS; FOLDING ENTROPY; DIMENSION; ATTRACTORS; FORMULA;

D O I：

10.1007/s00220-009-0859-4

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We prove that, for a C (2) non-invertible but non-degenerate map on a compact Riemannian manifold without boundary, an invariant measure satisfies an equality relating entropy, folding entropy and negative Lyapunov exponents. This generalizes Ledrappier-Young's entropy formula [5] (for negative Lyapunov exponents of diffeomorphisms) to the case of endomorphisms.

引用

页码：491 / 512

页数：22

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