Lyapunov Exponents and Invariant Measures on a Projective Bundle

被引：2

作者：

Osipenko, G. S. ^{[1
]}

机构：

[1] Lomonosov Moscow State Univ, Moscow, Russia

来源：

MATHEMATICAL NOTES | 2017年 / 101卷 / 3-4期

基金：

俄罗斯基础研究基金会;

关键词：

Morse spectrum; chain-recurrent set; projective bundle; invariant measure; symbolic image; flow on a graph; averaging with respect to a measure;

D O I：

10.1134/S0001434617030245

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A discrete dynamical system generated by a diffeomorphism f on a compact manifold is considered. The Morse spectrum is the limit set of Lyapunov exponents of periodic pseudotra-jectories. It is proved that the Morse spectrum coincides with the set of averagings of the function phi(x, e) - ln |Df(x)e| over the invariant measures of the mapping induced by the differential Df on the projective bundle.

引用

页码：666 / 676

页数：11

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