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Regularity of coboundaries for nonuniformly expanding Markov maps


Author: Sébastien Gouëzel
Journal: Proc. Amer. Math. Soc. 134 (2006), 391-401
MSC (2000): Primary 37A20, 37D25
DOI: https://doi.org/10.1090/S0002-9939-05-08145-1
Published electronically: September 21, 2005
MathSciNet review: 2176007
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Abstract: We prove that solutions $u$ of the equation $f=u-u\circ T$ are automatically Hölder continuous when $f$ is Hölder continuous and $T$ is nonuniformly expanding and Markov. This result applies in particular to Young towers and to intermittent maps.


References [Enhancements On Off] (What's this?)

  • [Aar97] Jon Aaronson.
    An introduction to infinite ergodic theory, volume 50 of Mathematical Surveys and Monographs.
    American Mathematical Society, 1997. MR 1450400 (99d:28025)
  • [AD01] Jon Aaronson and Manfred Denker.
    Local limit theorems for partial sums of stationary sequences generated by Gibbs-Markov maps.
    Stoch. Dyn., 1:193-237, 2001. MR 1840194 (2002h:37014)
  • [ADSZ04] Jon Aaronson, Manfred Denker, Omri Sarig, and Roland Zweimüller.
    Aperiodicity of cocycles and conditional local limit theorems.
    Stoch. Dyn., 4:31-62, 2004. MR 2069366 (2005e:37015)
  • [FHV03] Pierre Ferrero, Nicolai T.A. Haydn, and Sandro Vaienti.
    Entropy fluctuations for parabolic maps.
    Nonlinearity, 16:1203-1218, 2003. MR 1986291 (2004d:37009)
  • [GH88] Yves Guivarc'h and Jean Hardy.
    Théorèmes limites pour une classe de chaînes de Markov et applications aux difféomorphismes d'Anosov.
    Ann. Inst. H. Poincaré Probab. Statist., 24:73-98, 1988. MR 0937957 (89m:60080)
  • [Gou03] Sébastien Gouëzel.
    Berry-Esseen theorem and local limit theorem for non uniformly expanding maps.
    Preprint, 2003.
  • [Leo60] V. P. Leonov.
    On the central limit theorem for ergodic endomorphisms of compact commutative groups.
    Dokl. Akad. Nauk SSSR, 135:258-261, 1960. MR 0171302 (30:1533)
  • [Liv72] Alexander N. Livsic.
    Cohomology properties of dynamical systems.
    Math. USSR Izv., pages 1278-1301, 1972.
  • [Liv96] Carlangelo Liverani.
    Central limit theorems for deterministic systems.
    In International Conference on Dynamical Systems, Montevideo 1995, volume 362 of Pitman Research Notes in Mathematics, 1996. MR 1460797 (98k:28025)
  • [LSV99] Carlangelo Liverani, Benoît Saussol, and Sandro Vaienti.
    A probabilistic approach to intermittency.
    Ergodic Theory Dynam. Systems, 19:671-685, 1999. MR 1695915 (2000d:37029)
  • [NS03] Matthew Nicol and Andrew Scott.
    Livsic theorems and stable ergodicity for group extensions of hyperbolic systems with discontinuities.
    Ergodic Theory Dynam. Systems, 23:1867-1889, 2003. MR 2032492 (2004k:37051)
  • [PY99] Mark Pollicott and Michiko Yuri.
    Regularity of solutions to the measurable Livsic equation.
    Trans. Amer. Math. Soc., 351:559-568, 1999. MR 1621702 (99d:58110)
  • [Sar01] Omri Sarig.
    Thermodynamic formalism for null recurrent potentials.
    Israel J. Math., 121:285-311, 2001. MR 1818392 (2001m:37059)
  • [Sar03] Omri Sarig.
    Existence of Gibbs measures for countable Markov shifts.
    Proc. Amer. Math. Soc., 131(6):1751-1758, 2003. MR 1955261 (2004b:37056)
  • [Spi64] Frank Spitzer.
    Principles of random walk.
    The University Series in Higher Mathematics. D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London, 1964. MR 0171290 (30:1521)
  • [You99] Lai-Sang Young.
    Recurrence times and rates of mixing.
    Israel J. Math., 110:153-188, 1999. MR 1750438 (2001j:37062)

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Additional Information

Sébastien Gouëzel
Affiliation: Département de mathématiques et applications, École Normale Supérieure, 45 rue d’Ulm, 75005 Paris, France
Email: sebastien.gouezel@ens.fr

DOI: https://doi.org/10.1090/S0002-9939-05-08145-1
Received by editor(s): July 16, 2004
Published electronically: September 21, 2005
Communicated by: Michael Handel
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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