Abstract In this paper we investigate the quasi-shadowing property for C1 random dynamical sys-terns on their random partially hyperbolic sets. It is shown that for any pseudo orbit {xk}＋∞ -∞ on a random partially ...Abstract In this paper we investigate the quasi-shadowing property for C1 random dynamical sys-terns on their random partially hyperbolic sets. It is shown that for any pseudo orbit {xk}＋∞ -∞ on a random partially hyperbolic set there exists a ＂center＂ pseudo orbit {Yk}＋∞ -∞ shadowing it in the sense that yk＋l is obtained from the image of yk by a motion along the center direction. Moreover, when the random partially hyperbolic set has a local product structure, the above ＂center＂ pseudo orbit{yk}＋∞ -∞ can be chosen such that yk＋1 and the image of yk lie in their common center leaf.展开更多
A diffeomorphism is non-uniformly partially hyperbolic if it preserves an ergodic measure with at least one zero Lyapunov exponent.We prove that a C^(1)-smooth Z^(d)-action has the quasishadowing property if one of th...A diffeomorphism is non-uniformly partially hyperbolic if it preserves an ergodic measure with at least one zero Lyapunov exponent.We prove that a C^(1)-smooth Z^(d)-action has the quasishadowing property if one of the generators is C^(1+α)(α>0)non-uniformly partially hyperbolic.展开更多
基金supported by NSFC(Grant Nos.11371120 and 11771118)supported by Fundamental Research Funds for the Central University,China(Grant No.20720170004)
文摘Abstract In this paper we investigate the quasi-shadowing property for C1 random dynamical sys-terns on their random partially hyperbolic sets. It is shown that for any pseudo orbit {xk}＋∞ -∞ on a random partially hyperbolic set there exists a ＂center＂ pseudo orbit {Yk}＋∞ -∞ shadowing it in the sense that yk＋l is obtained from the image of yk by a motion along the center direction. Moreover, when the random partially hyperbolic set has a local product structure, the above ＂center＂ pseudo orbit{yk}＋∞ -∞ can be chosen such that yk＋1 and the image of yk lie in their common center leaf.
基金supported by the Science and Technology Research Program of Chongqing Municipal Education Commission(Grant No.KJQN202300802)the second author is supported by NSFC(Grant Nos.11801261,12071285)+1 种基金the third author is supported by NSFC(Grant Nos.11871120,12071082)Natural Science Foundation of Chongqing(Grant No.cstc2021jcyj-msxmX0299)。
文摘A diffeomorphism is non-uniformly partially hyperbolic if it preserves an ergodic measure with at least one zero Lyapunov exponent.We prove that a C^(1)-smooth Z^(d)-action has the quasishadowing property if one of the generators is C^(1+α)(α>0)non-uniformly partially hyperbolic.
