Accessibility and hyperbolicity (Q5954269)

This paper deals with accessibility and hyperbolicity properties for \(C^1\) surface diffeomorphisms. To this end the author checks conditions providing which point in the stable set of a hyperbolic invariant set for a \(C^1\) surface diffeomorphism is accessible via a path from the complement of the stable set. The author shows that \(z\in W^s(\Lambda)\) is accessible from \(M\setminus W^s(\Lambda)\) if and only if \(z\) lies on the stable manifold of a periodic point \(q\), and there is a branch of a local unstable manifold of \(q\) disjoint from \(W^s(\Lambda)\). Here by \(M\) is denoted the surface and by \(\Lambda\) a compact saturated hyperbolic locally stable closed invariant set possessing a local product structure.