Let f ： M → M be a partially hyperbolic diffeomorphism on a closed Riemannian manifold with uniformly compact center foliation. We show that if the center foliation of f is of dimension one then the topological entr...Let f ： M → M be a partially hyperbolic diffeomorphism on a closed Riemannian manifold with uniformly compact center foliation. We show that if the center foliation of f is of dimension one then the topological entropy is constant on a small C1 neighborhood of f.展开更多
We prove that the restrictions of the conjugacy between two Anosov diffeomorphisms of the twotorus to the stable and unstable manifolds are quasisymmetric homeomorphisms.
Embedding flows are used to obtain a rigidity result on strongly topological conjugacy of families of diffeomorphisms,i.e.families of C4(2≤r≤∞) diffeomorphisms,the strongly topologically conjugating homeomor-phisms...Embedding flows are used to obtain a rigidity result on strongly topological conjugacy of families of diffeomorphisms,i.e.families of C4(2≤r≤∞) diffeomorphisms,the strongly topologically conjugating homeomor-phisms near degenerate saddle-nodes will be differentiable on center manifolds of the saddle-nodes.展开更多
The purpose of this paper is to extend the concept topological entropy to nonautonomous linear systems. Next, we shall give estimation of the topological entropy for the class of bounded linear equations on Rn. Finall...The purpose of this paper is to extend the concept topological entropy to nonautonomous linear systems. Next, we shall give estimation of the topological entropy for the class of bounded linear equations on Rn. Finally, we are about to investigate the invariant properties of one through the transformations such as topological conjugacy, topological equivalence and kinematically similar and then show that topological entropy of one is equal to sum of positive Lyapunov characteristic exponents.展开更多
基金supported by NSFC(No:11371120)GCCHB(No:GCC2014052)supported by NSFHB(No:A2014205154)
文摘Let f ： M → M be a partially hyperbolic diffeomorphism on a closed Riemannian manifold with uniformly compact center foliation. We show that if the center foliation of f is of dimension one then the topological entropy is constant on a small C1 neighborhood of f.
文摘We prove that the restrictions of the conjugacy between two Anosov diffeomorphisms of the twotorus to the stable and unstable manifolds are quasisymmetric homeomorphisms.
基金Project supported by the National Natural Science Foundation of China and the Basic Science Research Foundation of Tsinghua University.
文摘Embedding flows are used to obtain a rigidity result on strongly topological conjugacy of families of diffeomorphisms,i.e.families of C4(2≤r≤∞) diffeomorphisms,the strongly topologically conjugating homeomor-phisms near degenerate saddle-nodes will be differentiable on center manifolds of the saddle-nodes.
文摘The purpose of this paper is to extend the concept topological entropy to nonautonomous linear systems. Next, we shall give estimation of the topological entropy for the class of bounded linear equations on Rn. Finally, we are about to investigate the invariant properties of one through the transformations such as topological conjugacy, topological equivalence and kinematically similar and then show that topological entropy of one is equal to sum of positive Lyapunov characteristic exponents.
