High dimension diffeomorphisms displaying infinitely many periodic attractors. (English) Zbl 0817.58004

Palis, J.; Viana, M.

Ann. Math. (2) 140, No. 1, 207-250 (1994).

The authors extend to higher dimensions the known two-dimensional result of S. E. Newhouse [Topology 13, 9-18 (1974; Zbl 0275.58016)] in the following main Theorem: Near any smooth diffeomorphism exhibiting a homoclinic tangency associated to a sectionally dissipative saddle, there is a residual subset of an open set of diffeomorphisms such that each of its elements displays infinitely many coexisting sinks (attracting periodic orbits).

Reviewer: B.V.Loginov (Ulyanovsk)

MSC:

58C25	Differentiable maps on manifolds
37C70	Attractors and repellers of smooth dynamical systems and their topological structure

Keywords:

periodic attractors; smooth diffeomorphism; homoclinic tangency; sinks

Citations:

Zbl 0275.58016