Super exponential growth of the number of periodic orbits inside homoclinic classes (Q928450)

The authors show that, quoting the abstract, ``there is a residual subset \(S(M)\) of \(\text{Diff}^1(M)\) such that, for every \(f\in S(M)\), any homoclinic class of \(f\) containing periodic saddles \(p\) and \(q\) of indices \(\alpha\) and \(\beta\) respectively, where \(\alpha<\beta\), has super-exponential growth of the number of periodic points inside the homoclinic class''. Furthermore, it is shown that the super-exponential growth occurs for hyperbolic periodic points of index \(\gamma\) inside the homoclinic class for every \(\gamma\in[\alpha,\beta]\).