Strange attractors in saddle-node cycles: prevalence and globality |
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| Authors: | L J Dı´az J Rocha M Viana |
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| Institution: | (1) Departamento Matemática PUC-RJ, Marque^s de S. Vicente 225, 22453-900 Rio de Janeiro, Brazil; e-mail: lodiaz@mat.puc-rio.br , BR;(2) Departamento de Matemática Pura, Faculdade de Cie^ncias, 4000 Porto, Portugal; e-mail: jrocha@fc.up.pt , PT;(3) IMPA, Est. D. Castorina 110, Jardim Bota^nico, 22460-320 Rio de Janeiro, Brazil; e-mail: viana@impa.br, BR |
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| Abstract: | We consider parametrized families of diffeomorphisms bifurcating through the creation of critical saddle-node cycles. We
show that they always exhibit Hénon-like strange attractors for a set of parameter values with positive Lebesgue density at
the bifurcation value. In open classes of such families the strange attractors are of global type: their basins contain an
a priori defined neighbourhood of the cycle. Furthermore, the bifurcation parameter may also be a point of positive density of hyperbolic
dynamics.
Oblatum VIII-1993 & 23-II-1995 |
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