Homoclinic classes with shadowing

Research

Jiweon Ahn¹, Keonhee Lee¹ and Manseob Lee²^*

¹ Department of Mathematics, Chungnam National University, Daejeon, 305-764, Korea

² Department of Mathematics, Mokwon University, Daejeon, 302-729, Korea

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Journal of Inequalities and Applications 2012, 2012:97 doi:10.1186/1029-242X-2012-97

Published: 23 April 2012

We show that for C¹generic diffeomorphisms, an isolated homoclinic class is shadow-able if and only if it is a hyperbolic basic set.

Mathematics Subject Classification 2000: 37C20; 37C05; 37C29; 37D05.

shadowing property; basic set; hyperbolic; generically; homoclinic class