In this paper, Brin-Katok local entropy formula and Katok＇s definition of the measuretheoretic entropy using spanning set are established for the random dynamical system over an invertible ergodic system.
For any C;diffeomorphism on a smooth compact Riemannian manifold that admits an ergodic measure with positive entropy,a lower bound of the Hausdorff dimension for the local stable and unstable sets is given in terms o...For any C;diffeomorphism on a smooth compact Riemannian manifold that admits an ergodic measure with positive entropy,a lower bound of the Hausdorff dimension for the local stable and unstable sets is given in terms of the measure-theoretic entropy and the maximal Lyapunov exponent.The main line of our approach to this result is under the setting of topological dynamical systems,which is also applicable to infinite-dimensional C;dynamical systems.展开更多
In this paper, we define and study polynomial entropy on an arbitrary subset and local measure theoretic polynomial entropy for any Borel probability measure on a compact metric space,and investigate the relation betw...In this paper, we define and study polynomial entropy on an arbitrary subset and local measure theoretic polynomial entropy for any Borel probability measure on a compact metric space,and investigate the relation between local measure-theoretic polynomial entropy of Borel probability measures and polynomial entropy on an arbitrary subset. Also, we establish a variational principle for polynomial entropy on compact subsets in the context of amenable group actions.展开更多
基金the National Natural Science Foundation of China(No.10701032)Natural Science Foundation of Hebei Province(No.A2008000132)
文摘In this paper, Brin-Katok local entropy formula and Katok＇s definition of the measuretheoretic entropy using spanning set are established for the random dynamical system over an invertible ergodic system.
基金supported by National Natural Science Foundation of China(Grant No.11701394)supported by National Natural Science Foundation of China(Grant Nos.11971455 and 11731003)supported by National Natural Science Foundation of China(Grant Nos.11671279 and 11541003)。
文摘For any C;diffeomorphism on a smooth compact Riemannian manifold that admits an ergodic measure with positive entropy,a lower bound of the Hausdorff dimension for the local stable and unstable sets is given in terms of the measure-theoretic entropy and the maximal Lyapunov exponent.The main line of our approach to this result is under the setting of topological dynamical systems,which is also applicable to infinite-dimensional C;dynamical systems.
基金supported by Foundation in higher education institutions of He’nan Province,P. R. China(Grant No. 23A110020)National Natural Science Foundation of China (Grant No. 11401363)+4 种基金the Foundation for the Training of Young Key Teachers in Colleges and Universities in He’nan Province,P. R. China (Grant No.2018GGJS134)supported by National Natural Science Foundation of China (Gratn No.11971236)China Postdoctoral Science Foundation (Grant No. 2016M591873)China Postdoctoral Science Special Foundation (Grant No. 2017T100384)funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions。
文摘In this paper, we define and study polynomial entropy on an arbitrary subset and local measure theoretic polynomial entropy for any Borel probability measure on a compact metric space,and investigate the relation between local measure-theoretic polynomial entropy of Borel probability measures and polynomial entropy on an arbitrary subset. Also, we establish a variational principle for polynomial entropy on compact subsets in the context of amenable group actions.
