Inverse shadowing and related measures  

作　　者：Sergey G.Kryzhevich Sergei Yu.Pilyugin 

机构地区：[1]Department of Mathematical Physics,Saint Petersburg State University,Saint Petersburg 199034,Russia [2]Department of Mathematics and Computer Science,Saint Petersburg State University,Saint Petersburg 199034,Russia

出　　处：《Science China Mathematics》2020年第9期1825-1836,共12页中国科学：数学（英文版）

基　　金：This work was supported by the Russian Foundation for Basic Researches(Grant No.18-01-00230-a).

摘　　要：We study various weaker forms of the inverse shadowing property for discrete dynamical systems on a smooth compact manifold.First,we introduce the so-called ergodic inverse shadowing property(Birkhoff averages of continuous functions along an exact trajectory and the approximating one are close).We demonstrate that this property implies the continuity of the set of invariant measures in the Hausdorff metric.We show that the class of systems with ergodic inverse shadowing is quite broad;it includes all diffeomorphisms with hyperbolic nonwandering sets.Second,we study the so-called individual inverse shadowing(any exact trajectory can be traced by approximate ones,but this shadowing is not uniform with respect to the initial point of the trajectory).We demonstrate that this property is closely related to structural stability andΩ-stability of diffeomorphisms.

关 键 词：inverse shadowing invariant measure HYPERBOLICITY axiom A STABILITY 

分 类 号：O186.11[理学—数学]