American Institute of Mathematical Sciences

Advanced
July  2005, 12(4): 639-656. doi: 10.3934/dcds.2005.12.639

Decay of correlations on towers with non-Hölder Jacobian and non-exponential return time

Jérôme Buzzi 1, and  Véronique Maume-Deschamps 2,

1. 

Centre de Mathématiques de l'Ecole Polytechnique, U.M.R. 7640 du C.N.R.S., Ecole Polytechnique, 91128 Palaiseau Cedex, France
2. 

Institut de Mathématiques de Bourgogne, Université de Bourgogne, 9, Avenue Alain Savary - B.P. 47870, 21078 Dijon Cedex, France

Received  March 2003 Revised  November 2004 Published  January 2005

We establish upper bounds on the rate of decay of correlations of tower systems with summable variation of the Jacobian and integrable return time. That is, we consider situations in which the Jacobian is not Hölder and the return time is only subexponentially decaying. We obtain a subexponential bound on the correlations, which is essentially the slowest of the decays of the variation of the Jacobian and of the return time.
Keywords: tower extension., equilibrium states, transfer operator, Absolutely continuous invariant measures, decay of correlations.
Mathematics Subject Classification: 37A25, 37A30, 47A3.
Citation: Jérôme Buzzi, Véronique Maume-Deschamps. Decay of correlations on towers with non-Hölder Jacobian and non-exponential return time. Discrete & Continuous Dynamical Systems - A, 2005, 12 (4) : 639-656. doi: 10.3934/dcds.2005.12.639
[1]

Ivan Werner. Equilibrium states and invariant measures for random dynamical systems. Discrete & Continuous Dynamical Systems - A, 2015, 35 (3) : 1285-1326. doi: 10.3934/dcds.2015.35.1285
[2]

Jiu Ding, Aihui Zhou. Absolutely continuous invariant measures for piecewise $C^2$ and expanding mappings in higher dimensions. Discrete & Continuous Dynamical Systems - A, 2000, 6 (2) : 451-458. doi: 10.3934/dcds.2000.6.451
[3]

Simon Lloyd, Edson Vargas. Critical covering maps without absolutely continuous invariant probability measure. Discrete & Continuous Dynamical Systems - A, 2019, 39 (5) : 2393-2412. doi: 10.3934/dcds.2019101
[4]

Christoph Bandt, Helena PeÑa. Polynomial approximation of self-similar measures and the spectrum of the transfer operator. Discrete & Continuous Dynamical Systems - A, 2017, 37 (9) : 4611-4623. doi: 10.3934/dcds.2017198
[5]

Jawad Al-Khal, Henk Bruin, Michael Jakobson. New examples of S-unimodal maps with a sigma-finite absolutely continuous invariant measure. Discrete & Continuous Dynamical Systems - A, 2008, 22 (1&2) : 35-61. doi: 10.3934/dcds.2008.22.35
[6]

Vítor Araújo. Semicontinuity of entropy, existence of equilibrium states and continuity of physical measures. Discrete & Continuous Dynamical Systems - A, 2007, 17 (2) : 371-386. doi: 10.3934/dcds.2007.17.371
[7]

Leandro Cioletti, Artur O. Lopes, Manuel Stadlbauer. Ruelle operator for continuous potentials and DLR-Gibbs measures. Discrete & Continuous Dynamical Systems - A, 2020, 40 (8) : 4625-4652. doi: 10.3934/dcds.2020195
[8]

Adrian Tudorascu. On absolutely continuous curves of probabilities on the line. Discrete & Continuous Dynamical Systems - A, 2019, 39 (9) : 5105-5124. doi: 10.3934/dcds.2019207
[9]

Lucia D. Simonelli. Absolutely continuous spectrum for parabolic flows/maps. Discrete & Continuous Dynamical Systems - A, 2018, 38 (1) : 263-292. doi: 10.3934/dcds.2018013
[10]

Michiko Yuri. Polynomial decay of correlations for intermittent sofic systems. Discrete & Continuous Dynamical Systems - A, 2008, 22 (1&2) : 445-464. doi: 10.3934/dcds.2008.22.445
[11]

Vincent Lynch. Decay of correlations for non-Hölder observables. Discrete & Continuous Dynamical Systems - A, 2006, 16 (1) : 19-46. doi: 10.3934/dcds.2006.16.19
[12]

Ioannis Konstantoulas. Effective decay of multiple correlations in semidirect product actions. Journal of Modern Dynamics, 2016, 10: 81-111. doi: 10.3934/jmd.2016.10.81
[13]

Dieter Mayer, Tobias Mühlenbruch, Fredrik Strömberg. The transfer operator for the Hecke triangle groups. Discrete & Continuous Dynamical Systems - A, 2012, 32 (7) : 2453-2484. doi: 10.3934/dcds.2012.32.2453
[14]

Dariusz Skrenty. Absolutely continuous spectrum of some group extensions of Gaussian actions. Discrete & Continuous Dynamical Systems - A, 2010, 26 (1) : 365-378. doi: 10.3934/dcds.2010.26.365
[15]

Stefano Galatolo, Pietro Peterlongo. Long hitting time, slow decay of correlations and arithmetical properties. Discrete & Continuous Dynamical Systems - A, 2010, 27 (1) : 185-204. doi: 10.3934/dcds.2010.27.185
[16]

Oliver Jenkinson. Optimization and majorization of invariant measures. Electronic Research Announcements, 2007, 13: 1-12.

[17]

Siniša Slijepčević. Stability of invariant measures. Discrete & Continuous Dynamical Systems - A, 2009, 24 (4) : 1345-1363. doi: 10.3934/dcds.2009.24.1345
[18]

Omri M. Sarig. Bernoulli equilibrium states for surface diffeomorphisms. Journal of Modern Dynamics, 2011, 5 (3) : 593-608. doi: 10.3934/jmd.2011.5.593
[19]

Dominic Veconi. Equilibrium states of almost Anosov diffeomorphisms. Discrete & Continuous Dynamical Systems - A, 2020, 40 (2) : 767-780. doi: 10.3934/dcds.2020061
[20]

Mark F. Demers, Hong-Kun Zhang. Spectral analysis of the transfer operator for the Lorentz gas. Journal of Modern Dynamics, 2011, 5 (4) : 665-709. doi: 10.3934/jmd.2011.5.665

2019 Impact Factor: 1.338

Tools

Metrics

  • PDF downloads (30)
  • HTML views (0)
  • Cited by (3)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences