This paper studies the M0-shadowing property for the dynamics of diffeomorphisms defined on closed manifolds. The C1 interior of the set of all two dimensional diffeomorphisms with the M0-shadowing property is describ...This paper studies the M0-shadowing property for the dynamics of diffeomorphisms defined on closed manifolds. The C1 interior of the set of all two dimensional diffeomorphisms with the M0-shadowing property is described by the set of all Anosov diffeomorphisms. The C1-stably M0-shadowing property on a non-trivial transitive set implies the diffeomorphism has a dominated splitting.展开更多
基金Supported by the National Natural Science Foundation of China(Grant Nos.11601449 and 11701328)Science and Technology Innovation Team of Education Department of Sichuan for Dynamical System and its Applications(Grant No.18TD0013)+3 种基金Youth Science and Technology Innovation Team of Southwest Petroleum University for Nonlinear Systems(Grant No.2017CXTD02)Scientific Research Starting Project of Southwest Petroleum University(Grant No.2015QHZ029)Shandong Provincial Natural Science Foundation,China(Grant No.ZR2017QA006)Young Scholars Program of Shandong University,Weihai(Grant No.2017WHWLJH09)
文摘This paper studies the M0-shadowing property for the dynamics of diffeomorphisms defined on closed manifolds. The C1 interior of the set of all two dimensional diffeomorphisms with the M0-shadowing property is described by the set of all Anosov diffeomorphisms. The C1-stably M0-shadowing property on a non-trivial transitive set implies the diffeomorphism has a dominated splitting.
