DIFFEOMORPHISMS WITH VARIOUS C^1 STABLE PROPERTIES  

作　　者：田学廷 孙文祥 

机构地区：[1]Academy of Mathematics and Systems Science,Chinese Academy of Sciences [2]Departamento de Matem'atica,Universidade Federal de Alagoas,Maceió 57072-090,Brazil [3]LMAM,School of Mathematical Sciences,Peking University

出　　处：《Acta Mathematica Scientia》2012年第2期552-558,共7页数学物理学报（B辑英文版）

基　　金：supported by CAPES(Brazil);supported by National Natural Science Foundation(10671006,10831003);National Basic Research Program of China(973 Program)(2006CB805903)

摘　　要：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.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.

关 键 词：Specification property hyperbolic basic set topologically transitive shad-owing property 

分 类 号：O186.12[理学—数学] O175.1[理学—基础数学]