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

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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

Abstract
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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

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