Orbital shadowing property on chain transitive sets for generic diffeomorphisms

Manseob Lee

doi:10.2478/ausm-2020-0009

Abstract

Let f : M → M be a diffeomorphism on a closed smooth n(≥ 2) dimensional manifold M. We show that C¹ generically, if a diffeomorphism f has the orbital shadowing property on locally maximal chain transitive sets which admits a dominated splitting then it is hyperbolic.

References

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Orbital shadowing property on chain transitive sets for generic diffeomorphisms

Abstract

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