Multidimensional nonhyperbolic attractors

Marcelo Viana

Publications Mathématiques de l'IHÉS (1997)

  • Volume: 85, page 63-96
  • ISSN: 0073-8301

How to cite


Viana, Marcelo. "Multidimensional nonhyperbolic attractors." Publications Mathématiques de l'IHÉS 85 (1997): 63-96. <>.

author = {Viana, Marcelo},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {nonuniform multidimensional expansion; positive Lyapunov exponents},
language = {eng},
pages = {63-96},
publisher = {Institut des Hautes Études Scientifiques},
title = {Multidimensional nonhyperbolic attractors},
url = {},
volume = {85},
year = {1997},

AU - Viana, Marcelo
TI - Multidimensional nonhyperbolic attractors
JO - Publications Mathématiques de l'IHÉS
PY - 1997
PB - Institut des Hautes Études Scientifiques
VL - 85
SP - 63
EP - 96
LA - eng
KW - nonuniform multidimensional expansion; positive Lyapunov exponents
UR -
ER -


  1. [BC1] M. BENEDICKS, L. CARLESON, On iterations of 1 - ax2 on (-1, 1), Ann. Math. 122 (1985), 1-25. Zbl0597.58016MR87c:58058
  2. [BC2] M. BENEDICKS, L. CARLESON, The dynamics of the Hénon map, Ann. Math. 133 (1991), 73-169. Zbl0724.58042MR92d:58116
  3. [BY] M. BENEDICKS, L.-S. YOUNG, SBR-measures for certain Hénon maps, Invent. Math. 112-3 (1993), 541-576. Zbl0796.58025MR94e:58074
  4. [BD] C. BONATTI, L. J. DÍAZ, Persistent nonhyperbolic transitive diffeomorphisms, Ann. Math. 143 (1996), 357-396. Zbl0852.58066MR97d:58122
  5. [CE] P. COLLET, J.-P. ECKMANN, On the abundance of aperiodic behaviour, Comm. Math. Phys. 73 (1980), 115-160. Zbl0441.58011MR82c:58035
  6. [HPS] M. HIRSCH, C. PUGH, M. SHUB, Invariant Manifolds, Lect. Notes Math. 583 (1977), Springer Verlag. Zbl0355.58009MR58 #18595
  7. [Ja] M. JAKOBSON, Absolutely continuous invariant measures for one-parameter families of one-dimensional maps, Comm. Math. Phys. 81 (1981), 39-88. Zbl0497.58017MR83j:58070
  8. [Ma] R. MAÑÉ, Contributions to the stability conjecture, Topology 17 (1978), 383-396. Zbl0405.58035MR84b:58061
  9. [MS] W. DE MELO, S. VAN STRIEN, One-Dimensional Dynamics, Springer Verlag, 1993. Zbl0791.58003MR95a:58035
  10. [MV] L. MORA, M. VIANA, Abundance of strange attractors, Acta Math. 171 (1993), 1-71. Zbl0815.58016MR94k:58089
  11. [No] T. NOWICKI, A positive Lyapunov exponent for the critical value of an S-unimodal mapping implies uniform hyperbolicity, Ergod. Th. & Dynam. Sys. 8 (1988), 425-435. Zbl0638.58021MR90c:58100
  12. [Sh] M. SHUB, Topologically transitive diffeomorphisms on T4, Lect. Notes in Math. 206 (1971), 39, Springer Verlag. 
  13. [Si] D. SINGER, Stable orbits and bifurcations of maps of the interval, SIAM J. Appl. Math. 35 (1978), 260-267. Zbl0391.58014MR58 #13206
  14. [Sm] S. SMALE, Differentiable dynamical systems, Bull. Am. Math. Soc. 73 (1967), 747-817. Zbl0202.55202MR37 #3598
  15. [Vi] M. VIANA, Strange attractors in higher dimensions, Bull. Braz. Math. Soc. 24 (1993), 13-62. Zbl0784.58044MR94k:58093
  16. [Yo] L.-S. YOUNG, Some open sets of nonuniformly hyperbolic cocycles, Ergod. Th. & Dynam. Sys. 13 (1993), 409-415. Zbl0797.58041MR94k:58106

Citations in EuDML Documents

  1. Sébastien Gouëzel, Decay of correlations for nonuniformly expanding systems
  2. José Ferreira Alves, SRB measures for non-hyperbolic systems with multidimensional expansion
  3. Rodrigo Bamón, Jan Kiwi, Juan Rivera-Letelier, Richard Urzúa, On the topology of solenoidal attractors of the cylinder
  4. Viviane Baladi, Michael Benedicks, Véronique Maume-Deschamps, Almost sure rates of mixing for i.i.d. unimodal maps
  5. José F. Alves, Stefano Luzzatto, Vilton Pinheiro, Markov structures and decay of correlations for non-uniformly expanding dynamical systems
  6. Jérôme Buzzi, Puzzles of Quasi-Finite Type, Zeta Functions and Symbolic Dynamics for Multi-Dimensional Maps
  7. Mario Ponce, Sur la persistance des courbes invariantes pour les dynamiques holomorphes fibrées lisses
  8. J. Palis, A global perspective for non-conservative dynamics

NotesEmbed ?


You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.


Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.