@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://archive.numdam.org/item/AST_2013__358__13_0/} }
TY - CHAP AU - Avila, Artur AU - Santamaria, Jimmy AU - Viana, Marcelo TI - Holonomy invariance: rough regularity and applications to Lyapunov exponents BT - Cocycles over partially hyperbolic maps AU - Collectif T3 - Astérisque PY - 2013 SP - 13 EP - 74 IS - 358 PB - Société mathématique de France UR - http://archive.numdam.org/item/AST_2013__358__13_0/ LA - en ID - AST_2013__358__13_0 ER -
%0 Book Section %A Avila, Artur %A Santamaria, Jimmy %A Viana, Marcelo %T Holonomy invariance: rough regularity and applications to Lyapunov exponents %B Cocycles over partially hyperbolic maps %A Collectif %S Astérisque %D 2013 %P 13-74 %N 358 %I Société mathématique de France %U http://archive.numdam.org/item/AST_2013__358__13_0/ %G en %F AST_2013__358__13_0
Avila, Artur; Santamaria, Jimmy; Viana, Marcelo. Holonomy invariance: rough regularity and applications to Lyapunov exponents, in Cocycles over partially hyperbolic maps, Astérisque, no. 358 (2013), pp. 13-74. http://archive.numdam.org/item/AST_2013__358__13_0/
[1] Simplicity of Lyapunov spectra: a sufficient criterion", Port. Math. (N.S.) 64 (2007), p. 311-376. | DOI | MR | Zbl
& - "[2] Simplicity of Lyapunov spectra: proof of the Zorich-Kontsevich conjecture", Acta Math. 198 (2007), p. 1-56. | DOI | MR | Zbl
& - "[3] Extremal Lyapunov exponents: an invariance principle and applications", Invent. Math. 181 (2010), p. 115-178. | DOI | MR | Zbl
& - "[4] Absolute continuity, Lyapunov exponents and rigidity I: geodesic flows", preprint arXiv:1110.2365. | DOI | MR | Zbl
, & - "[5] Convergence of probability measures, John Wiley & Sons Inc., 1968. | MR | Zbl
-[6] Lyapunov exponents: how frequently are dynamical systems hyperbolic?", in Modern dynamical systems and applications, Cambridge Univ. Press, 2004, p. 271-297. | MR | Zbl
& - "[7] 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] Lyapunov exponents with multiplicity 1 for deterministic products of matrices", Ergodic Theory Dynam. Systems 24 (2004), p. 1295-1330. | DOI | MR | Zbl
& - "[9] Partially hyperbolic dynamical systems", Izv. Acad. Nauk. SSSR 38 (1974), p. 170-212. | MR | Zbl
& - "[10] On the ergodicity of partially hyperbolic systems", Ann. of Math. 171 (2010), p. 451-489. | DOI | MR | Zbl
& - "[11] Conformally natural extension of homeomorphisms of the circle", Acta Math. 157 (1986), p. 23-48. | DOI | MR | Zbl
& - "[12] Noncommuting random products", Trans. Amer. Math. Soc. 108 (1963), p. 377-428. | DOI | MR | Zbl
- "[13] Products of random matrices", Ann. Math. Statist. 31 (1960), p. 457-469. | DOI | MR | Zbl
& - "[14] Adapted metrics for dominated splittings", Ergodic Theory Dynam. Systems 27 (2007), p. 1839-1849. | DOI | MR | Zbl
- "[15] 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] Invariant manifolds, Lecture Notes in Math., vol. 583, Springer, 1977. | MR | Zbl
, & -[17] Fibre bundles, third ed., Graduate Texts in Math., vol. 20, Springer, 1994. | MR
-[18] The ergodic theory of subadditive stochastic processes", J. Roy. Statist. Soc. Ser. B 30 (1968), p. 499-510. | MR | Zbl
- "[19] 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] Stably ergodic dynamical systems and partial hyperbolicity", J. Complexity 13 (1997), p. 125-179. | DOI | MR | Zbl
& - "[21] Stable ergodicity and julienne quasi-conformality", J. Eur. Math. Soc. (JEMS) 2 (2000), p. 1-52. | DOI | EuDML | MR | Zbl
& - "[22] Creation of blenders in the conservative setting", Nonlinearity 23 (2010), p. 211-223. | DOI | MR | Zbl
, , & - "[23] On the fundamental ideas of measure theory", Mat. Sbornik N.S. 25 (67) (1949), p. 107-150. | MR
- "[24] Global stability of dynamical systems, Springer, 1987. | MR | Zbl
-[25] Almost all cocycles over any hyperbolic system have nonvanishing Lyapunov exponents", Ann. of Math. 167 (2008), p. 643-680. | DOI | MR | Zbl
- "[26] 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] The cohomological equation for partially hyperbolic diffeomorphisms", preprint arXiv:0809.4862. | Numdam | MR | Zbl
- "