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High dimension diffeomorphisms exhibiting infinitely many strange attractors

Abstract:

In this work we show, on a manifold of any dimension, that arbitrarily near any smooth diffeomorphism with a homoclinic tangency associated to a sectionally dissipative fixed or periodic point (i.e. the product of any pair of eigenvalues has norm less than 1), there exists a diffeomorphism exhibiting infinitely many Hénon-like strange attractors. In the two-dimensional case this has been proved in [E. Colli, Infinitely many coexisting strange attractors, Ann. Inst. H. Poincaré Anal. Non Linéaire 15 (1998) 539-579]. We also show that a parametric version of this result is true. © 2007 Elsevier Masson SAS. All rights reserved.