Let M be a smooth compact manifold and A be a compact invariant set. In this article, we prove that, for every robustly transitive set A, flA satisfies a Cl-genericstable shadowable property （resp., Cl-generic-stable...Let M be a smooth compact manifold and A be a compact invariant set. In this article, we prove that, for every robustly transitive set A, flA satisfies a Cl-genericstable shadowable property （resp., Cl-generic-stable transitive specification property or Cl-generic-stable barycenter property） if and only if A is a hyperbolic basic set. In particular, flA satisfies a Cl-stable shadowable property （resp., Cl-stable transitive specification property or Cl-stable barycenter property） if and only if A is a hyperbolic basic set. Similar results are valid for volume-preserving case.展开更多
基金supported by CAPES(Brazil)supported by National Natural Science Foundation(10671006,10831003)National Basic Research Program of China(973 Program)(2006CB805903)
文摘Let M be a smooth compact manifold and A be a compact invariant set. In this article, we prove that, for every robustly transitive set A, flA satisfies a Cl-genericstable shadowable property （resp., Cl-generic-stable transitive specification property or Cl-generic-stable barycenter property） if and only if A is a hyperbolic basic set. In particular, flA satisfies a Cl-stable shadowable property （resp., Cl-stable transitive specification property or Cl-stable barycenter property） if and only if A is a hyperbolic basic set. Similar results are valid for volume-preserving case.
