Comptes Rendus
no. 10
Dynamical Systems
A remark on conservative diffeomorphisms
[Une remarque sur les difféomorphismes conservatifs]

Présenté par : Étienne Ghys

Jairo Bochi1 ; Bassam R. Fayad2 ; Enrique Pujals3
1 Inst. Matemática, UFRGS, Av Bento Gonçalves 9500, 91509-900 Porto Alegre, Brazil
2 LAGA, université Paris 13, 99, avenue J.-B. Clément, 93430 Villetaneuse, France
3 IMPA, Estr. D. Castorina 110, 22460-320 Rio de Janeiro, Brazil
Comptes Rendus. Mathématique, Volume 342 (2006) no. 10, pp. 763-766.

On montre qu'un difféomorphisme stablement ergodique peut être C1 approché par un difféomorphisme ayant des exposants de Lyapunov stablement non-nuls.

We show that a stably ergodic diffeomorphism can be C1 approximated by a diffeomorphism having stably non-zero Lyapunov exponents.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2006.03.028
Jairo Bochi 1 ; Bassam R. Fayad 2 ; Enrique Pujals 3

1 Inst. Matemática, UFRGS, Av Bento Gonçalves 9500, 91509-900 Porto Alegre, Brazil
2 LAGA, université Paris 13, 99, avenue J.-B. Clément, 93430 Villetaneuse, France
3 IMPA, Estr. D. Castorina 110, 22460-320 Rio de Janeiro, Brazil 
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     title = {A remark on conservative diffeomorphisms},
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     pages = {763--766},
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     language = {en},
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Jairo Bochi; Bassam R. Fayad; Enrique Pujals. A remark on conservative diffeomorphisms. Comptes Rendus. Mathématique, Volume 342 (2006) no. 10, pp. 763-766. doi : 10.1016/j.crma.2006.03.028. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.03.028/

[1] A. Arbieto, C. Matheus, A pasting lemma and some applications for conservative systems, Ergodic Theory Dynam. Systems, in press

[2] L. Arnold Random Dynamical Systems, Springer-Verlag, New York, 1998

[3] J. Bochi Genericity of zero Lyapunov exponents, Ergodic Theory Dynam. Systems, Volume 22 (2002), pp. 1667-1696

[4] J. Bochi; M. Viana The Lyapunov exponents of generic volume preserving and symplectic maps, Ann. of Math., Volume 161 (2005), pp. 1423-1485

[5] C. Bonatti; A.T. Baraviera Removing zero Lyapunov exponents, Ergodic Theory Dynam. Systems, Volume 23 (2003), pp. 1655-1670

[6] C. Bonatti; L. Díaz; E. Pujals A C1-generic dichotomy for diffeomorphisms: weak forms of hyperbolicity or infinitely many sinks or sources, Ann. of Math., Volume 158 (2003), pp. 355-418

[7] C. Bonatti; M. Viana SRB measures for partially hyperbolic systems whose central direction is mostly contracting, Israel J. Math., Volume 115 (2000), pp. 157-193

[8] K. Burns; D. Dolgopyat; Ya. Pesin Partial hyperbolicity, Lyapunov exponents, and stable ergodicity, J. Statist. Phys., Volume 108 (2002), pp. 927-942

[9] D. Dolgopyat; Ya. Pesin Every compact manifold carries a completely hyperbolic diffeomorphism, Ergodic Theory Dynam. Systems, Volume 22 (2002), pp. 409-435

[10] M. Grayson; C. Pugh; M. Shub Stably ergodic diffeomorphisms, Ann. of Math., Volume 140 (1994), pp. 295-329

[11] F. Ledrappier Propriétés ergodiques des mesures de Sinaï, Publ. Math. IHES, Volume 59 (1984), pp. 163-188

[12] M. Shub; A. Wilkinson Pathological foliations and removable zero exponents, Invent. Math., Volume 139 (2000), pp. 495-508

[13] A. Tahzibi Stably ergodic diffeomorphisms which are not partially hyperbolic, Israel J. Math., Volume 142 (2004), pp. 315-344

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