Orbital shadowing property on chain transitive sets for generic diffeomorphisms

Manseob Lee
2020 Acta Universitatis Sapientiae: Mathematica  
AbstractLet 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.
doi:10.2478/ausm-2020-0009 fatcat:payzh3lx3fd2boxjjmbqp37erq