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
In this paper,we study unstable topological pressure for C^(1)-smooth partially hyperbolic diffeomorphisms with sub-additive potentials.Moreover,without any additional assumption,we have established the expected varia...In this paper,we study unstable topological pressure for C^(1)-smooth partially hyperbolic diffeomorphisms with sub-additive potentials.Moreover,without any additional assumption,we have established the expected variational principle which connects this unstable topological pressure and the unstable measure theoretic entropy,as well as the corresponding Lyapunov exponent.展开更多
In this paper, we give some definitions of the topological tail pressures for sub-additive potentials and prove that they are equivalent if the potentials are continuous. Under some assumptions, we get a variational p...In this paper, we give some definitions of the topological tail pressures for sub-additive potentials and prove that they are equivalent if the potentials are continuous. Under some assumptions, we get a variational principle which exhibits the relationship between topological tail pressure and measure-theoretic tail entropy. Finally, we define a new measure-theoretic tail pressure for sub-additive potentials and some interesting properties of it are obtained.展开更多
In this paper, we prove that some volume-preserving almost Anosov systems are ergodic if they are essentially accessible. The key idea is that there are stable and unstable manifolds with uniform size on the orbits Of...In this paper, we prove that some volume-preserving almost Anosov systems are ergodic if they are essentially accessible. The key idea is that there are stable and unstable manifolds with uniform size on the orbits Of the hyperbolic points for these systems.展开更多
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.
基金supported by NSFC (Grant No. 11501066)Department of Education in Chongqing City (Grant Nos. KJQN201900724 and KJQN202100722)+2 种基金supported by Natural Science Foundation of Chongqing,China (Grant No. cstc2021jcyj-msxmX1042)Chongqing Key Laboratory of Analytic Mathematics and Applications in Chongqing Universitysupported by NSFC(Grant Nos. 11871120 and 11671093)
文摘In this paper,we study unstable topological pressure for C^(1)-smooth partially hyperbolic diffeomorphisms with sub-additive potentials.Moreover,without any additional assumption,we have established the expected variational principle which connects this unstable topological pressure and the unstable measure theoretic entropy,as well as the corresponding Lyapunov exponent.
基金Supported by NSFC(Grant No.11471056)Foundation and Frontier Research Program of Chongqing(Grant No.cstc2016jcyjA0312)
文摘In this paper, we give some definitions of the topological tail pressures for sub-additive potentials and prove that they are equivalent if the potentials are continuous. Under some assumptions, we get a variational principle which exhibits the relationship between topological tail pressure and measure-theoretic tail entropy. Finally, we define a new measure-theoretic tail pressure for sub-additive potentials and some interesting properties of it are obtained.
基金Supported by National Natural Science Foundation of China(Grant No.11001284)Natural Science FoundationProject of CQ CSTC(Grant No.cstcjjA00003)Fundamental Research Funds for Central Universities(CDJZR10100006)
文摘In this paper, we prove that some volume-preserving almost Anosov systems are ergodic if they are essentially accessible. The key idea is that there are stable and unstable manifolds with uniform size on the orbits Of the hyperbolic points for these systems.
