[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.14403/jcms.2018.31.1.461

SOME SHADOWING PROPERTIES OF THE SHIFTS ON THE INVERSE LIMIT SPACES

Tsegmid, Nyamdavaa (Department of Mathematics Chungnam National University)

Publication Information

Journal of the Chungcheong Mathematical Society / v.31, no.4, 2018 , pp. 461-466 More about this Journal

Abstract

$Let\;f:X{\rightarrow}X$ be a continuous surjection of a compact metric space X and let ${\sigma}_f:X_f{\rightarrow}X_f$ be the shift map on the inverse limit space $X_f$ constructed by f. We show that if a continuous surjective map f has some shadowing properties: the asymptotic average shadowing property, the average shadowing property, the two side limit shadowing property, then ${\sigma}_f$ also has the same properties.

Keywords

inverse limit space; shift map; two-sided limit; average shadowing; asymptotic average shadowing property;

Citations & Related Records

Times Cited By KSCI : 1 (Citation Analysis)

Reference
Cited By KSCI

1	N. Aoki and K. Hiriade, Topological Theory of Dynamical Systems, Recent Advances, North-Holland, 1994.
2	A. Barzanouni, Inverse Limit Spaces with Various Shadowing Property, J. Math. 2014 (2014), 4pages. http://dx.doi.org/10.1155/2014/169183 DOI
3	B. Carvalho and D. Kwietniak, On homeomorphisms with the two-sided limit shadowing property, J. Math. Anal. Appl. 420 (2014), no. 1, 801-813 DOI
4	L. Chen and S. Li, Shadowing Property for Inverse Limit Spaces, Proc. Amer. Math. Soc. 115 (1992), no. 1, 573-580. DOI
5	R. Gu, The asymptotic average shadowing property and transitivity, Nonlinear Anal. 67 (2007), no. 6, 1680-1689 DOI
6	J. Park and Y. Zhang, Average shadowing properties on compact metric spaces, Commun. Korean Math. Soc. 21 (2006), no. 2, 355-361. DOI
7	M. Lee, Various shadowing properties for inverse limit systems, J. Chungcheong. Math. Soc. 29 (2016), no. 4, 657-661 DOI
8	S. Li, Dynamical properties of the shift maps on the inverse limit spaces, Ergodic Theory and Dynam. Systems, 12 (1992), no. 1, 95-108. DOI
9	E. Shah and T. K. Das, On shadowing property for inverse limit spaces, Math. Slovaca, 58 (2008),no. 1, 95-100. DOI
10	Y. Zhang, On the average-shadowing property, Acta Sci. Natur. Univ. Pekinensis, 37 (2001), no. 5, 648-651. DOI