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

Jérôme Buzzi; Véronique Maume-Deschamps

doi:10.3934/dcds.2005.12.639

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2005, Volume 12, Issue 4: 639-656. Doi: 10.3934/dcds.2005.12.639

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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
2.
Institut de Mathématiques de Bourgogne, Université de Bourgogne, 9, Avenue Alain Savary - B.P. 47870, 21078 Dijon Cedex

Received: March 2003

Revised: November 2004

Published: July 2005

Abstract / Introduction Related Papers Cited by

Abstract

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:

Absolutely continuous invariant measures,
equilibrium states,
decay of correlations,
transfer operator,
tower extension.

Mathematics Subject Classification: 37A25, 37A30, 47A35.

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