High dimension diffeomorphisms exhibiting infinitely many strange attractors

Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

Volumn 25, Issue 3, 2008, Pages 587-607

  Leal, Bladismir ^a  

^a FACULTAD DE CIENCIAS   (Venezuela)

Author keywords

Diffeomorphisms; Homoclinic tangency; Strange attractors

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; PARAMETER ESTIMATION;

DIFFEOMORPHISMS; HOMOCLINIC TANGENCY; STRANGE ATTRACTORS;

NONLINEAR ANALYSIS;

EID: 43049145034     PISSN: 02941449     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.anihpc.2007.03.002     Document Type: Article

References (16)

1. M. Benedicks L. Carleson The dynamics of the Hénon map Ann. of Math. 133 1991 73 169
2. E. Colli Infinitely many coexisting strange attractors Ann. Inst. H. Poincaré Anal. Non Linéaire 15 1998 539 579
3. M. Hénon A two dimensional mapping with a strange attractor Comm. Math. Phys. 50 1976 69 77
4. L. Mora M. Viana Abundance of strange attractors Acta Math. 171 1993 1 71
5. S. Newhouse Diffeomorphisms with infinitely many sinks Topology 13 1974 9 18
6. S. Newhouse The abundance of wild hyperbolic sets and nonsmooth stable sets for diffeomorphisms Publ. Math. I.H.E.S. 50 1979 101 151
7. J. Palis A global view of Dynamics and a conjecture on the denseness of finitude of attractors Géométrie complexe et systèmes dynamiques Orsay, 1995 Astérisque 261 2000 335 347
8. J. Palis A global perspective for non-conservative dynamics Ann. Inst. H. Poincaré Anal. Non Linéaire 22 2005 485 507
9. J. Palis F. Takens Hyperbolicity and Sensitive-Chaotic Dynamics at Homoclinic Bifurcations 1993 Cambridge University Press
10. J. Palis M. Viana High dimension diffeomorphisms displaying infinitely many periodic attractors Ann. of Math. 140 1994 207 250
11. A. Pumariño J.A. Rodriguez Coexistence and persistence of infinitely many strange attractors Ergodic Theory Dynam. Systems 21 2001 1511 1523
12. S. Smale Differentiable dynamical systems Bull. Amer. Math. Soc. 73 1967 747 817
13. E. Sternberg On the structure of local homeomorphisms of euclidean n -space – II Amer. J. Math. 80 1958 623 631
14. C. Tresser J.M. Gambaudo Diffeomorphisms with infinitely many strange attractors J. Complexity 6 1990 409 416
15. M. Viana Strange attractors in higher dimensions Bull. Braz. Math. Soc. 24 1993 13 62
16. J.A. Yorke K.T. Alligood Cascades of period doubling bifurcations a prerequisite for horseshoes Bull. Amer. Math. Soc. 9 1983 319 322