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Persistence of homoclinic tangencies in higher dimensions. (English) Zbl 0833.58020
The author extends to a very general context Newhouse’s phenomenon concerning the persistence of homoclinic tangencies and the coexistence of infinitely many sinks. The technique used by the author is based on one-dimensional analogues of the mentioned phenomenon proved by J. Palis and M. Viana. As a consequence of the reduction of codimension in homoclinic tangencies, the following results are obtained:
1. Existence of cascades of periodic doubling bifurcation in any codimension.
2. Abundance of what we call strangles, saddle-sets in generic families unfolding a homoclinic tangency of codimension two and higher.
Reviewer: S.Nenov (Sofia)

MSC:
37B99 Topological dynamics
37J40 Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol’d diffusion
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