Lyapunov exponent,Liao perturbation and persistence  

作　　者：Wenxiang Sun Todd Young 

机构地区：[1]School of Mathematical Sciences,Peking University,Beijing 100871,China [2]Department of Mathematics,Ohio University,Athens,OH 45701,USA

出　　处：《Science China Mathematics》2020年第9期1913-1928,共16页中国科学：数学（英文版）

基　　金：The rst author was supported by National Natural Science Foundation of China(Grant Nos.11771026 and 11831001).

摘　　要：Consider a C1 vector eld together with an ergodic invariant probability that hasℓnonzero Lya-punov exponents.Using orthonormal moving frames along a generic orbit we construct a linear system ofℓdi erential equations which is a linearized Liao standard system.We show that Lyapunov exponents of this linear system coincide with all the nonzero exponents of the given vector eld with respect to the given ergodic probability.Moreover,we prove that these Lyapunov exponents have a persistence property meaning that a small perturbation to the linear system(Liao perturbation)preserves both the sign and the value of the nonzero Lyapunov exponents.

关 键 词：Lyapunov exponent Liao perturbation ergodic probability non-uniformly hyperbolicity 

分 类 号：O186.1[理学—数学]