Weak Strictly Persistence Homeomorphisms and Weak Inverse Shadowing Property and Genericity

• Journal title : Kyungpook mathematical journal
• Volume 49, Issue 3,  2009, pp.411-418
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2009.49.3.411
Title & Authors
Weak Strictly Persistence Homeomorphisms and Weak Inverse Shadowing Property and Genericity

Abstract
In this paper we introduce the notions of strict persistence and weakly strict persistence which are stronger than those of persistence and weak persistence, respectively, and study their relations with shadowing property. In particular, we show that the weakly strict persistence and the weak inverse shadowing property are locally generic in Z(M).
Keywords
inverse shadowing property;persistence $\small{{\delta}}$-pseudo-orbit;shadowing property;
Language
English
Cited by
1.
Inverse Shadowing and Weak Inverse Shadowing Property, Applied Mathematics, 2012, 03, 05, 478
References
1.
J. Lewowicz, Persistence in expansive systems, Ergodic Theory Dynam. Systems, 3(1983), 567-578.

2.
T. Choi, S. Kim, K. Lee, Weak inverse shadowing and genericity, Bull. Korean Math. Soc., 43(1)(2006), 43-52.

3.
B. Honary, A. Zamani Bahabadi, Orbital shadowing property, Bull. Korean Math. Soc., 45(4)(2008), 645-650.

4.
P. Walters, On the pseudo orbit tracing property and its relationship to stability, Lecture Notes in Math., Vol. 668, Springer, Berlin, 1978, 231-244.

5.
R. Corless and S. Plyugin, Approximate and real trajectories for generic dynamical systems, J. Math. Anal. Appl., 189(1995), 409-423.

6.
P. Diamond, P. Kloeden, V. Korzyakin and A. Pokrovskii, Computer robustness of semihypebolic mappings, Random and computational Dynamics, 3(1995), 53-70.

7.
P. Kloeden, J. Ombach and A. Pokroskii, Continuous and inverse shadowing, Functional Differential Equations, 6(1999), 137-153.

8.
K. Lee, Continuous inverse shadowing and hyperbolicity, Bull. Austral. Math. Soc., 67(2003), 15-26.

9.
P. Diamond, Y. Han and K. Lee, Bishadowing and hyperbolicity, International Journal of Bifuractions and chaos, 12(2002), 1779-1788.

10.
K. Kuratowski, "Topology2", AcademicPress-PWN-PolishSciencePublishers, Warszawa, 1968. MR0259835(41 4467).