[KSCI] Korea Science Citation Index Service

Lee, Manseob (Department of Mathematics Mokwon University)

Publication Information

Abstract

In this paper, we show that if a quasi-Anosov diffeomorphism has the various types of shadowing property then it is Anosov.

Keywords

shadowing; asymptotic average shadowing; average shadowing; ergodic shadowing; chain transitive; quasi-Anosov;

Citations & Related Records

Times Cited By KSCI : 1 (Citation Analysis)

1	R. Mane, Quasi-Anosov diffeomorphisms and hyperbolic manifolds, Trans. Amer. Math. Soc. 38 (1980), 192-209.
2	J. Palis, On the $C^1$ -stability conjecture, IHES Publ. Math. 66 (1988), 211-215.
3	M. L. Blank, Metric properties of ${\epsilon}$ -trajectories of dynamical systems with stochastic behaviour, Ergod. Th. Dynam. Syst. 8 (1988), 365-378.
4	A. Fakhari and F. H. Ghane, On shadowing: ordinary and ergodic, J. Math. Anal. Appl. 364 (2010), 151-155. DOI
5	M. Lee and J. Park, Diffeomorphisms with Average and Asymptotic Average Shadowing, Dynam. Contin. Discrete and Impulsive Systems, Series A: Math. Anal. 23 (2016) 285-294.
6	J. Franks and C. Robinson, A quasi-Anosov diffeomorphism that is not Anosov, Tran. Amer. Math. Soc. 223 (1976), 267-278. DOI
7	J. Franks and J. Selgrade, Hyperbolicity and chain recurrence, J. Diff. Eqaut. 26 (1977), 27-36. DOI
8	R. Gu, The asymptotic average shadowing property and transitivity, Nonlinear Anal. 67 (2007), 1680-1689. DOI
9	M. Lee, Robustly chain transitive diffeomorphisms, J. Inequal. Appl. 2015, 2015:230, 1-6.
10	J. Park and Y. Zhang, Average shadowing properties on compact metric spaces, Commun. Korean Math. Soc. 21 (2006), 355-361. DOI
11	K. Sakai, Quasi-Anosov diffeomorphisms and pseudo-orbit tracing property, Nagoya Math. J. 111 (1988), 111-114. DOI