Resumen de Local Topological Stability for Diffeomorphisms

Manseob Lee

• Let f : M → M be a diffeomorphism of compact smooth Riemannian manifold M, an let ⊂ M be a closed f -invariant set. We obtain conditions for to be topologically stable which is called -topologically stable. Moreover, we prove that if f is C1 robustly -topologically stable then satisfies star condition for f . Then in the above, if a closed f -invariant set is chain transitive (or transitive) then it is hyperbolic for f .