Seeking conjugate invariant is one of significant and general topics on dynamical systems. Few invariants have been found so far. Topological entropy is one of such invariants. Studies about the topological entropy ar...Seeking conjugate invariant is one of significant and general topics on dynamical systems. Few invariants have been found so far. Topological entropy is one of such invariants. Studies about the topological entropy are concentrated on areas of homeomorphisms and one-dimensional continuous self-maps. In this note we consider Anosov maps, a sort of continuous maps on general compact metric spaces. By using a finite subshift and the largest positive eigenvalue we will calculate the topological entropy for Anosov maps.展开更多
We present a sufficient and necessary condition for the subshift of finite type to be a measure-preserving transformation or to be a strong mixing measure-preserving transformation with respect to the Hausdorff measur...We present a sufficient and necessary condition for the subshift of finite type to be a measure-preserving transformation or to be a strong mixing measure-preserving transformation with respect to the Hausdorff measure. It is proved that a strong mixing subshift of finite type has a chaotic set with full Hausdorff measure.展开更多
文摘Seeking conjugate invariant is one of significant and general topics on dynamical systems. Few invariants have been found so far. Topological entropy is one of such invariants. Studies about the topological entropy are concentrated on areas of homeomorphisms and one-dimensional continuous self-maps. In this note we consider Anosov maps, a sort of continuous maps on general compact metric spaces. By using a finite subshift and the largest positive eigenvalue we will calculate the topological entropy for Anosov maps.
基金Supported by National Natural Science Foundation of China （Grant No. 60763009）
文摘We present a sufficient and necessary condition for the subshift of finite type to be a measure-preserving transformation or to be a strong mixing measure-preserving transformation with respect to the Hausdorff measure. It is proved that a strong mixing subshift of finite type has a chaotic set with full Hausdorff measure.
