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 sp...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.展开更多
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).
文摘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.
