Hyperbolicity of \(C^1\)-stably expansive homoclinic classes
The authors consider Diff\((M)\) - the space of diffeomorphisms of the compact \(C^{\infty}\) manifold, endowed with the \(C^1\)-topology. It is shown in the main result of the paper that if there exists some residual subset \(R\subset\text{ Diff}(M)\) such that for any \(f\in R\) and a hyperbolic periodic point \(p\) of \(f\), the homoclinic class \(H_f(p)\) is \(C^{\infty}\)-stable expansive iff it is \(C^{\infty}\)-persistently expansive.
scientific article; zbMATH DE number 5725428