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,a definition of entropy for Z＋k（k≥2）-actions due to Friedland is studied.Unlike the traditional definition,it may take a nonzero value for actions whose generators have finite（even zero） entropy as...In this paper,a definition of entropy for Z＋k（k≥2）-actions due to Friedland is studied.Unlike the traditional definition,it may take a nonzero value for actions whose generators have finite（even zero） entropy as single transformations.Some basic properties are investigated and its value for the Z＋k-actions on circles generated by expanding endomorphisms is given.Moreover,an upper bound of this entropy for the Z＋k-actions on tori generated by expanding endomorphisms is obtained via the preimage entropies,which are entropy-like invariants depending on the ＂inverse orbits＂ structure of the system.展开更多
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 National Natural Science Foundation of China(Grant No.11071054)the Key Project of Chinese Ministry of Education(Grant No.211020)+1 种基金the Program for New Century Excellent Talents in University(Grant No.11-0935)the Project Sponsored by the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry(Grant No.11126011)
文摘In this paper,a definition of entropy for Z＋k（k≥2）-actions due to Friedland is studied.Unlike the traditional definition,it may take a nonzero value for actions whose generators have finite（even zero） entropy as single transformations.Some basic properties are investigated and its value for the Z＋k-actions on circles generated by expanding endomorphisms is given.Moreover,an upper bound of this entropy for the Z＋k-actions on tori generated by expanding endomorphisms is obtained via the preimage entropies,which are entropy-like invariants depending on the ＂inverse orbits＂ structure of the system.
