Inventiones mathematicae

, Volume 125, Issue 1, pp 37–74

Strange attractors in saddle-node cycles: prevalence and globality

  • L. J. Dı´az
  • J. Rocha
  • M. Viana

DOI: 10.1007/s002220050068

Cite this article as:
Dı´az, L., Rocha, J. & Viana, M. Invent math (1996) 125: 37. doi:10.1007/s002220050068

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.

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • L. J. Dı´az
    • 1
  • J. Rocha
    • 2
  • M. Viana
    • 3
  1. 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. 2.Departamento de Matemática Pura, Faculdade de Cie^ncias, 4000 Porto, Portugal; e-mail: jrocha@fc.up.pt PT
  3. 3.IMPA, Est. D. Castorina 110, Jardim Bota^nico, 22460-320 Rio de Janeiro, Brazil; e-mail: viana@impa.brBR