@incollection{AST_2013__358__75_0, author = {Wilkinson, Amie}, title = {The cohomological equation for partially hyperbolic diffeomorphisms}, booktitle = {Cocycles over partially hyperbolic maps}, series = {Ast\'erisque}, pages = {75--165}, publisher = {Soci\'et\'e math\'ematique de France}, number = {358}, year = {2013}, mrnumber = {3203217}, zbl = {1348.37054}, language = {en}, url = {http://archive.numdam.org/item/AST_2013__358__75_0/} }
TY - CHAP AU - Wilkinson, Amie TI - The cohomological equation for partially hyperbolic diffeomorphisms BT - Cocycles over partially hyperbolic maps AU - Collectif T3 - Astérisque PY - 2013 SP - 75 EP - 165 IS - 358 PB - Société mathématique de France UR - http://archive.numdam.org/item/AST_2013__358__75_0/ LA - en ID - AST_2013__358__75_0 ER -
%0 Book Section %A Wilkinson, Amie %T The cohomological equation for partially hyperbolic diffeomorphisms %B Cocycles over partially hyperbolic maps %A Collectif %S Astérisque %D 2013 %P 75-165 %N 358 %I Société mathématique de France %U http://archive.numdam.org/item/AST_2013__358__75_0/ %G en %F AST_2013__358__75_0
Wilkinson, Amie. The cohomological equation for partially hyperbolic diffeomorphisms, dans Cocycles over partially hyperbolic maps, Astérisque, no. 358 (2013), pp. 75-165. http://archive.numdam.org/item/AST_2013__358__75_0/
[1] Cocycles over partially hyperbolic maps", this volume. | Numdam | Zbl
, & - "[2] Extremal Lyapunov exponents of smooth cocycles", Informes de matemática 606 (2008), https://www.researchgate.net/publication/ 228797868_Extremal_Lyapunov_exponents_of_smooth_cocycles. | Zbl
& - "[3] Absolute continuity, Lyapunov exponents and rigidity I: geodesic flows", preprint arXiv:1110.2365. | DOI | MR | Zbl
, & - "[4] Lyapunov exponents with multiplicity 1 for deterministic products of matrices", Ergodic Theory Dynam. Systems 24 (2004), p. 1295-1330. | DOI | MR | Zbl
& - "[5] Partially hyperbolic dynamical systems", Izv. Akad. Nauk SSSR Ser. Mat. 38 (1974), p. 170-212. | MR | Zbl
& - "[6] Stable ergodicity and Anosov flows", Topology 39 (2000), p. 149-159. | DOI | MR | Zbl
, & -"[7] Density of accessibility for partially hyperbolic diffeomorphisms with one-dimensional center", Discrete Contin. Dyn. Syst. 22 (2008), p. 75-88. | DOI | MR | Zbl
, , , & - "[8] Stable ergodicity of skew products", Ann. Sci. École Norm. Sup. 32 (1999), p. 859-889. | DOI | EuDML | Numdam | MR | Zbl
& - "[9] On the ergodicity of partially hyperbolic diffeomorphisms", to appear in Ann. of Math. | MR
& - "[10] Proprietà di una famiglia di spazi funzionali", Ann. Scuola Norm. Sup. Pisa 18 (1964), p. 137-160. | EuDML | Numdam | MR | Zbl
- "[11] Periodic cycle functionals and cocycle rigidity for certain partially hyperbolic actions", Discrete Contin. Dyn. Syst. 13 (2005), p. 985-1005. | DOI | MR | Zbl
& - "[12] Local rigidity of partially hyperbolic actions. II: The geometric method and restrictions of Weyl chamber flows on ", Int. Math. Res. Not. 2011 (2011), p. 4405-4430. | MR | Zbl
& - "[13] Livsič theory for compact group extensions of hyperbolic systems", Mosc. Math. J. 5 (2005), p. 55-67. | DOI | MR | Zbl
-"[14] Stable accessibility is dense", Astérisque 287 (2003), p. 33-60. | Numdam | MR | Zbl
& - "[15] On the cohomology of certain dynamical systems", Topology 19 (1980), p. 291-299. | DOI | MR | Zbl
& - "[16] Some inverse spectral results for negatively curved -manifolds", Topology 19 (1980), p. 301-312. | DOI | MR | Zbl
& - "[17] Differential topology, Graduate Texts in Math., vol. 33, Springer, 1994. | MR
-[18] Invariant manifolds, Lecture Notes in Math., vol. 583, Springer, 1977. | MR | Zbl
, & -[19] A regularity lemma for functions of several variables", Rev. Mat. Iberoamericana 4 (1988), p. 187-193. | DOI | EuDML | MR | Zbl
- "[20] Cocycles' stability for partially hyperbolic systems", Math. Res. Lett. 3 (1996), p. 191-210. | DOI | MR | Zbl
& - "[21] Rigidity of higher rank abelian cocycles with values in diffeomorphism groups", Geom. Dedicata 124 (2007), p. 109-131. | DOI | MR | Zbl
& - "[22] Natural operations in differential geometry, Springer, 1993. | DOI | MR | Zbl
, & -[23] Certain properties of the homology of -systems", Mat. Zametki 10 (1971), p. 555-564. | MR | Zbl
- "[24] Cohomology of dynamical systems", Izv. Akad. Nauk SSSR Ser. Mat. 36 (1972), p. 1296-1320. | MR
- "[25] Invariant measures that are compatible with smoothness for transitive -systems", Dokl. Akad. Nauk SSSR 207 (1972), p. 1039-1041. | MR | Zbl
& - "[26] Analytic regularity of solutions of Livsic's cohomology equation and some applications to analytic conjugacy of hyperbolic dynamical systems", Ergodic Theory Dynam. Systems 17 (1997), p. 649-662. | DOI | MR | Zbl
- "[27] Bootstrap of regularity for integrable solutions of cohomology equations", in Modern dynamical systems and applications, Cambridge Univ. Press, 2004, p. 405-418. | MR | Zbl
- "[28] Canonical perturbation theory of Anosov systems and regularity results for the Livšic cohomology equation", Ann. of Math. 123 (1986), p. 537-611. | DOI | MR | Zbl
, & - "[29] Livšic's theorem for semisimple Lie groups", Ergodic Theory Dynam. Systems 21 (2001), p. 1501-1509. | DOI | MR | Zbl
& - "[30] Whitney regularity for solutions to the coboundary equation on Cantor sets", Math. Phys. Electron. J. 13 (2007), Paper 6. | EuDML | MR | Zbl
& - "[31] Regularity of the transfer map for cohomologous cocycles", Ergodic Theory Dynam. Systems 18 (1998), p. 1187-1209. | DOI | MR | Zbl
& - "[32] Stably ergodic dynamical systems and partial hyperbolicity", J. Complexity 13 (1997), p. 125-179. | DOI | MR | Zbl
& - "[33] Hölder foliations", Duke Math. J. 86 (1997), p. 517-546. | DOI | MR | Zbl
, & - "[34] Correction to: "Hölder foliations" [Duke Math. J. 86 (1997), no. 3, 517-546; MR1432307 (97m:58155)]", Duke Math. J. 105 (2000), p. 105-106. | DOI | MR | Zbl
, & - "[35] -homogeneous compacta in are -submanifolds of ", Proc. Amer. Math. Soc. 124 (1996), p. 1219-1226. | DOI | MR | Zbl
, & - "[36] Accessibility and stable ergodicity for partially hyperbolic diffeomorphisms with -center bundle", Invent. Math. 172 (2008), p. 353-381. | DOI | MR | Zbl
, & - "[37] Periodic points and invariant pseudomeasures for toral endomorphisms", Ergodic Theory Dynam. Systems 6 (1986), p. 449-473. | DOI | MR | Zbl
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