[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.14403/jcms.2011.24.4.2

DIFFEOMORPHISMS WITH ROBUSTLY AVERAGE SHADOWING

Lee, Keonhee (Department of Mathematics Chungnam University)
Lee, Manseob (Department of Mathematics Mokwon University)
Lu, Gang (Department of Mathematics Chungnam University)

Publication Information

Journal of the Chungcheong Mathematical Society / v.24, no.4, 2011 , pp. 631-638 More about this Journal

Abstract

In this paper, we prove that for $C^1$ generically, if every hyperbolic periodic point in a chain component is uniformly far away from being nonhyperbolic, and it is $C^1$ -robustly average shadowable, then the chain component is hyperbolic.

Keywords

average shadowing; hyperbolic; chain component; homoclinic class; generic; stably hyperbolic;

Citations & Related Records

Reference

1	C. Bonatti and S. Crovisier, Recurrence and genericity, Invent. Math. 158 (2004), 33-104.
2	M. Hurley, Bifurcation and chain recurrence, Ergodic Thoery & Dynam. Syst. 3 (1983), 231-240.
3	M. Lee, Stably average shadowabe homoclinic classes, Nonlinear Anal.: Theory, Methods & Appl. 74 (2011), 689-694. DOI ScienceOn
4	R. Mane, An ergodic closing lemma, Ann. Math. 116 (1982), 503-540. DOI ScienceOn
5	X. Wen, S. Gan and L. Wen, $C^{1}$ -stably shadowble chain components are hyper-bolic, J. Differen. Equat. 246 (2009) 340-357. 159-175. DOI ScienceOn