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

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).

MSC:

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

Citations:

Zbl 0275.58016
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