Infinitely many coexisting strange attractors
The paper deals with an answer to a question in \(C^\infty\) topology and in the context of unfoldings of homoclinic tangencies of surface diffeomorphisms. The author proves that \(C^\infty\) diffeomorphisms of a two-dimensional manifold \(M\) with a homoclinic tangency are in the closure of an open set of \(\text{Diff}^\infty(M)\) containing a dense subset of diffeomorphisms exhibiting infinitely many coexisting Hénon-like strange attractors (or repellers). The author performs a renormalization scheme in 2-cycles of periodic points with a heteroclinic tangency. This renormalization is needed to control orbits, which in turn is essential to guarantee space for arbitrary small \(C^r\) perturbations, for any \(r\geq 0\).
scientific article; zbMATH DE number 1199909
scientific article