Holonomy invariance: rough regularity and applications to Lyapunov exponents

Avila, Artur ; Santamaria, Jimmy ; Viana, Marcelo

Cocycles over partially hyperbolic maps, Astérisque, no. 358 (2013), pp. 13-74.

@incollection{AST_2013__358__13_0,
     author = {Avila, Artur and Santamaria, Jimmy and Viana, Marcelo},
     title = {Holonomy invariance: rough regularity and applications to {Lyapunov} exponents},
     booktitle = {Cocycles over partially hyperbolic maps},
     series = {Ast\'erisque},
     pages = {13--74},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {358},
     year = {2013},
     mrnumber = {3203216},
     zbl = {1348.37005},
     language = {en},
     url = {http://www.numdam.org/item/AST_2013__358__13_0/}
}

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%A Viana, Marcelo
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%B Cocycles over partially hyperbolic maps
%A Collectif
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Avila, Artur; Santamaria, Jimmy; Viana, Marcelo. Holonomy invariance: rough regularity and applications to Lyapunov exponents, dans Cocycles over partially hyperbolic maps, Astérisque, no. 358 (2013), pp. 13-74. http://www.numdam.org/item/AST_2013__358__13_0/

Bibliographie
Cité par

[1] A. Avila & M. Viana - "Simplicity of Lyapunov spectra: a sufficient criterion", Port. Math. (N.S.) 64 (2007), p. 311-376. | DOI | MR | Zbl

[2] A. Avila & M. Viana - "Simplicity of Lyapunov spectra: proof of the Zorich-Kontsevich conjecture", Acta Math. 198 (2007), p. 1-56. | DOI | MR | Zbl

[3] A. Avila & M. Viana - "Extremal Lyapunov exponents: an invariance principle and applications", Invent. Math. 181 (2010), p. 115-178. | DOI | MR | Zbl

[4] A. Avila, M. Viana & A. Wilkinson - "Absolute continuity, Lyapunov exponents and rigidity I: geodesic flows", preprint arXiv:1110.2365. | DOI | MR | Zbl

[5] P. Billingsley - Convergence of probability measures, John Wiley & Sons Inc., 1968. | MR | Zbl

[6] J. Bochi & M. Viana - "Lyapunov exponents: how frequently are dynamical systems hyperbolic?", in Modern dynamical systems and applications, Cambridge Univ. Press, 2004, p. 271-297. | MR | Zbl

[7] C. Bonatti, X. Gómez-Mont & M. Viana - "Généricité d'exposants de Lyapunov non-nuls pour des produits déterministes de matrices", Ann. Inst. H. Poincaré Anal. Non Linéaire 20 (2003), p. 579-624. | DOI | EuDML | Numdam | MR | Zbl

[8] C. Bonatti & M. Viana - "Lyapunov exponents with multiplicity 1 for deterministic products of matrices", Ergodic Theory Dynam. Systems 24 (2004), p. 1295-1330. | DOI | MR | Zbl

[9] M. Brin & Y. Pesin - "Partially hyperbolic dynamical systems", Izv. Acad. Nauk. SSSR 38 (1974), p. 170-212. | MR | Zbl

[10] K. Burns & A. Wilkinson - "On the ergodicity of partially hyperbolic systems", Ann. of Math. 171 (2010), p. 451-489. | DOI | MR | Zbl

[11] A. Douady & C. J. Earle - "Conformally natural extension of homeomorphisms of the circle", Acta Math. 157 (1986), p. 23-48. | DOI | MR | Zbl

[12] H. Furstenberg - "Noncommuting random products", Trans. Amer. Math. Soc. 108 (1963), p. 377-428. | DOI | MR | Zbl

[13] H. Furstenberg & H. Kesten - "Products of random matrices", Ann. Math. Statist. 31 (1960), p. 457-469. | DOI | MR | Zbl

[14] N. Gourmelon - "Adapted metrics for dominated splittings", Ergodic Theory Dynam. Systems 27 (2007), p. 1839-1849. | DOI | MR | Zbl

[15] M. W. Hirsch & C. C. Pugh - "Stable manifolds and hyperbolic sets", in Global Analysis (Proc. Sympos. Pure Math., Vol. XIV, Berkeley, Calif., 1968), Amer. Math. Soc., 1970, p. 133-163. | MR | Zbl

[16] M. W. Hirsch, C. C. Pugh & M. Shub - Invariant manifolds, Lecture Notes in Math., vol. 583, Springer, 1977. | MR | Zbl

[17] D. Husemoller - Fibre bundles, third ed., Graduate Texts in Math., vol. 20, Springer, 1994. | MR

[18] J. F. C. Kingman - "The ergodic theory of subadditive stochastic processes", J. Roy. Statist. Soc. Ser. B 30 (1968), p. 499-510. | MR | Zbl

[19] F. Ledrappier - "Positivity of the exponent for stationary sequences of matrices", in Lyapunov exponents (Bremen, 1984), Lecture Notes in Math., vol. 1186, Springer, 1986, p. 56-73. | DOI | MR | Zbl

[20] C. Pugh & M. Shub - "Stably ergodic dynamical systems and partial hyperbolicity", J. Complexity 13 (1997), p. 125-179. | DOI | MR | Zbl

[21] C. Pugh & M. Shub - "Stable ergodicity and julienne quasi-conformality", J. Eur. Math. Soc. (JEMS) 2 (2000), p. 1-52. | DOI | EuDML | MR | Zbl

[22] F. Rodriguez Hertz, M. A. Rodriguez Hertz, A. Tahzibi & R. Ures - "Creation of blenders in the conservative setting", Nonlinearity 23 (2010), p. 211-223. | DOI | MR | Zbl

[23] V. A. Rohlin - "On the fundamental ideas of measure theory", Mat. Sbornik N.S. 25 (67) (1949), p. 107-150. | MR

[24] M. Shub - Global stability of dynamical systems, Springer, 1987. | MR | Zbl

[25] M. Viana - "Almost all cocycles over any hyperbolic system have nonvanishing Lyapunov exponents", Ann. of Math. 167 (2008), p. 643-680. | DOI | MR | Zbl

[26] M. Viana & J. Yang - "Physical measures and absolute continuity for one-dimensional center direction", Ann. Inst. H. Poincaré Anal. Non Linéaire 30 (2013), p. 845-877. | DOI | Numdam | MR | Zbl

[27] A. Wilkinson - "The cohomological equation for partially hyperbolic diffeomorphisms", preprint arXiv:0809.4862. | Numdam | MR | Zbl