$C^2$ diffeomorphisms with the inverse shadowing property
Commun. Korean Math. Soc. 2010 Vol. 25, No. 2, 257-262
https://doi.org/10.4134/CKMS.2010.25.2.257
Published online June 1, 2010
Manseob Lee
Mokwon University
Abstract : Let $f$ be a $C^2$-diffeomorphism on a closed surface which satisfies the Axiom A. Then $f$ is in the $C^2$-interior of the set of all diffeomorphisms having the inverse shadowing property with respect to the class of the continuous methods if and only if $f$ satisfies the strong transversality condition.
Keywords : Axiom A, shadowing property, inverse shadowing, strong transversality condition, hyperbolic, basic set
MSC numbers : 37D20, 37C50
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