A Type of the Shadowing Properties for Generic View Points

Axioms

Manseob Lee¹ 

[1] Department of Mathematics, Mokwon University, Daejeon 302-729, Korea;

关键词: average shadowing;    asymptotic average shadowing;    generic;    chain transitive;    Axiom A;    singular Axiom A;    Anosov;   

DOI  :  10.3390/axioms7010018

来源: DOAJ

【 摘 要 】

We show that if a C 1 generic diffeomorphism of a closed smooth two-dimensional manifold has the average shadowing property or the asymptotic average shadowing property, then it is Anosov. Moreover, if a C 1 generic vector field of a closed smooth three-dimensional manifold has the average shadowing property or the asymptotic average shadowing property, then it satisfies singular Axiom A without cycles.

【 授权许可】

Unknown