IJPAM: Volume 115, No. 1 (2017)
Department of Mathematics
Daejeon, 302-729, KOREA
be a closed smooth manifold, and let be a diffeomorphism on Let be a weakly transitive set for . First, we show that has the -stably shadowing property on if and only if is a hyperbolic basic set. Finally, we prove that for -generic a locally maximal weakly transitive set is shadowable if and only if that weakly transitive set is a hyperbolic basic set.
Received: March 3, 2017
Revised: June 28, 2017
Published: June 29, 2017
AMS Subject Classification: 37C20, 37C25, 37C50, 34D10
Key Words and Phrases: shadowing, hyperbolic, weakly transitive, transitive set, basic set
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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Pages: 169 - 186