Smoothness of invariant manifolds and foliations for in nite dimensional random dynamical systems--Dedicated to Professor Shantao Liao  

作　　者：Jun Shen Kening Lu Weinian Zhang 

机构地区：[1]Department of Mathematics,Sichuan University,Chengdu 610064,China [2]Department of Mathematics,Brigham Young University,Provo,UT 84602,USA

出　　处：《Science China Mathematics》2020年第9期1877-1912,共36页中国科学：数学（英文版）

基　　金：This work was supported by National Natural Science Foundation of China(Grant Nos.11501549,11331007,11971330,11771307,11831012 and 11726623);the Fundamental Research Funds for the Central Universities(Grant No.YJ201646).

摘　　要：In this paper,we investigate the smoothness of invariant manifolds and foliations for random dynamical systems with nonuniform pseudo-hyperbolicity in Hilbert spaces.We discuss on the effect of temperedness and the spectral gaps in the nonuniform pseudo-hyperbolicity so as to prove the existence of invariant manifolds and invariant foliations,which preserve the CN,τ;(ω)Holder smoothness of the random system in the space variable and the measurability of the random system in the sample point.Moreover,we also prove that the stable foliation is CN-1;(ω)in the base point.

关 键 词：random dynamical system invariant manifold invariant foliation pseudo-hyperbolicity MEASURABILITY 

分 类 号：O211.6[理学—概率论与数理统计] O186.1[理学—数学]