Let M be a closed smooth manifold M, and let f ： M → M be a diffeomorphism. In this paper, we consider a nontrivial transitive set A of f. We show that if f has the C^1-stably average shadowing property on A, then A...Let M be a closed smooth manifold M, and let f ： M → M be a diffeomorphism. In this paper, we consider a nontrivial transitive set A of f. We show that if f has the C^1-stably average shadowing property on A, then A admits a dominated splitting.展开更多
We study the mean orbital pseudo-metric for Polish dynamical systems and its connections with properties of the space of invariant measures.We give equivalent conditions for when the set of invariant measures generate...We study the mean orbital pseudo-metric for Polish dynamical systems and its connections with properties of the space of invariant measures.We give equivalent conditions for when the set of invariant measures generated by periodic points is dense in the set of ergodic measures and the space of invariant measures.We also introduce the concept of asymptotic orbital average shadowing property and show that it implies that every non-empty compact connected subset of the space of invariant measures has a generic point.展开更多
基金supported by Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education,Science and Technology(Grant No.2011-0007649)supported by National Natural Science Foundation of China(Grant No.11026041)
文摘Let M be a closed smooth manifold M, and let f ： M → M be a diffeomorphism. In this paper, we consider a nontrivial transitive set A of f. We show that if f has the C^1-stably average shadowing property on A, then A admits a dominated splitting.
基金Supported by NNSF of China(Grant Nos.12222110 and 12171298)。
文摘We study the mean orbital pseudo-metric for Polish dynamical systems and its connections with properties of the space of invariant measures.We give equivalent conditions for when the set of invariant measures generated by periodic points is dense in the set of ergodic measures and the space of invariant measures.We also introduce the concept of asymptotic orbital average shadowing property and show that it implies that every non-empty compact connected subset of the space of invariant measures has a generic point.
