Infinitely many coexisting strange attractors
Annales de l'I.H.P. Analyse non linéaire (1998)
- Volume: 15, Issue: 5, page 539-579
- ISSN: 0294-1449
Access Full Article
topHow to cite
topColli, Eduardo. "Infinitely many coexisting strange attractors." Annales de l'I.H.P. Analyse non linéaire 15.5 (1998): 539-579. <http://eudml.org/doc/78448>.
@article{Colli1998,
author = {Colli, Eduardo},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {homoclinic tangency; unfoldings; Hénon-like strange attractor; heteroclinic tangency; perturbation},
language = {eng},
number = {5},
pages = {539-579},
publisher = {Gauthier-Villars},
title = {Infinitely many coexisting strange attractors},
url = {http://eudml.org/doc/78448},
volume = {15},
year = {1998},
}
TY - JOUR
AU - Colli, Eduardo
TI - Infinitely many coexisting strange attractors
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1998
PB - Gauthier-Villars
VL - 15
IS - 5
SP - 539
EP - 579
LA - eng
KW - homoclinic tangency; unfoldings; Hénon-like strange attractor; heteroclinic tangency; perturbation
UR - http://eudml.org/doc/78448
ER -
References
top- [1] M. Benedicks and L. Carleson, The dynamics of the Hénon map, Ann. Math., Vol. 133, 1991, pp. 73-169. Zbl0724.58042MR1087346
- [2] E. Catsigeras, Cascades of period doubling of stable codimension one, Thesis IMPA, 1995.
- [3] J.-M. Gambaudo and C. Tresser, Diffeomorphisms with infinitely many strange attractors, J. of Complexity, Vol. 6, 1990, pp. 409-416. Zbl0717.58041MR1085387
- [4] R. Kraft, Intersection of thick Cantor sets, Mem. Amer. Math. Soc., Vol. 97, No. 468(2), 1992, pp. 1-119. Zbl0753.28009MR1106988
- [5] S. Newhouse, Non-density of Axiom A(a) on S2, Proc. A.M.S. Symp. Pure Math., Vol. 14, 1970, pp. 191-202. Zbl0206.25801MR277005
- [6] S. Newhouse, Diffeomorphisms with infinitely many sinks, Topology, Vol. 13, 1974, pp. 9-18. Zbl0275.58016MR339291
- [7] S. Newhouse, The abundance of wild hyperbolic sets and nonsmooth stable sets for diffeomorphisms, Publ. Math. I.H.E.S., Vol. 50, 1979, pp. 101-151. Zbl0445.58022MR556584
- [8] S. Newhouse, J. Palis and F. Takens, Bifurcations and stability of families of diffeomorphisms, Publ. Math. I.H.E.S., Vol. 57, 1983, pp. 5-71. Zbl0518.58031MR699057
- [9] L. Mora and M. Viana, Abundance of strange attractors, Acta Math., Vol. 171, 1993, pp. 1-71. Zbl0815.58016MR1237897
- [10] H. Poincaré, Sur le problème des trois corps et les equations de la dynamique (Mémoire couronné du prise de S.M. le roi Oscar II de Suède), Acta Math., Vol. 13, 1890, pp. 1-270. JFM22.0907.01
- [11] A. PUMARIÑO and J.A. Rodriguez, Coexistence and persistence of strange attractors, 1994, to appear. Zbl0877.58041MR1456717
- [12] J. Palis and F. Takens. Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations, Cambridge University Press, 1993. Zbl0790.58014MR1237641
- [13] C. Robinson, Bifurcation to infinitely many sinks, Comm. Math. Phys., Vol. 90, 1983, pp. 433-459. Zbl0531.58035MR719300
- [14] S. Sternberg, Local contractions and a theorem of Poincaré, Amer. J. Math., Vol. 79, 1957, pp. 809-824. Zbl0080.29902MR96853
- [15] S. Sternberg, On the structure of local homeomorphisms of Euclidean n-space, II, Amer. J. Math., Vol. 80, 1958, pp. 623-631. Zbl0083.31406MR96854
- [16] R. Ures, Approximating a Hénon-like strange attractor by a homoclinic tangency and an attracting cycle, to appear in Erg. Th. and Dyn. Syst.
- [17] M. Viana, Strange attractors in higher dimensions, Bol. Soc. Bras. Mat., Vol. 24(1), 1993, pp. 13-62. Zbl0784.58044MR1224299
- [18] J.A. Yorke and K.T. Alligood, Cascades of period doubling bifurcations: a pre-requisite for horseshoes, Bull. A.M.S., Vol. 9, 1983, pp. 319-322. Zbl0541.58039MR714994
Citations in EuDML Documents
top- Bladismir Leal, High dimension diffeomorphisms exhibiting infinitely many strange attractors
- Vítor Araújo, Attractors and time averages for random maps
- Jacob Palis, Jean-Christophe Yoccoz, Non-uniformly hyperbolic horseshoes arising from bifurcations of Poincaré heteroclinic cycles
- J. Palis, A global perspective for non-conservative dynamics
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.