Structurally stable homoclinic classes (Q256187)

Let \(p\) be a hyperbolic periodic point of a diffeomorphism \(f\). Consider the set \(H(p,f)\) which is the closure of the set of transverse intersections of the stable and unstable manifolds of the orbit of \(p\). The set \(H(p,f)\) is called the homoclinic class of \(p\). The author defines structural stability of a homoclinic class and shows thatNEWLINE{\parindent=0.7cmNEWLINE\begin{itemize}\item[(i)] a structurally stable homoclinic class admits a dominated splitting; NEWLINE\item[(ii)] a codimension-one homoclinic class is hyperbolic;NEWLINE\item[(iii)] if \(f\) is far from homoclinic tangencies, then its structurally stable homoclinic classes are hyperbolic.NEWLINENEWLINE\end{itemize}}