Rates of mixing for potentials

of summable variation

Author:
Mark Pollicott

Journal:
Trans. Amer. Math. Soc. **352** (2000), 843-853

MSC (1991):
Primary 58Fxx

Published electronically:
September 17, 1999

MathSciNet review:
1621698

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: It is well known that for subshifts of finite type and equilibrium measures associated to Hölder potentials we have exponential decay of correlations. In this article we derive explicit rates of mixing for equilibrium states associated to more general potentials.

**1.**Rufus Bowen,*Equilibrium states and the ergodic theory of Anosov diffeomorphisms*, Lecture Notes in Mathematics, Vol. 470, Springer-Verlag, Berlin-New York, 1975. MR**0442989****2.**N. I. Chernov,*Markov approximations and decay of correlations for Anosov flows*, Ann. of Math. (2)**147**(1998), no. 2, 269–324. MR**1626741**, 10.2307/121010**3.**M. I. Gordin,*The central limit theorem for stationary processes*, Dokl. Akad. Nauk SSSR**188**(1969), 739–741 (Russian). MR**0251785****4.**A. Kachurovskii,*Rate of convergence in ergodic theorems*, Russian Math. Surveys**51:4**(1996), 73-124. CMP**97:05****5.**Abdelaziz Kondah, Véronique Maume, and Bernard Schmitt,*Vitesse de convergence vers l’état d’équilibre pour des dynamiques markoviennes non höldériennes*, Ann. Inst. H. Poincaré Probab. Statist.**33**(1997), no. 6, 675–695 (French, with English and French summaries). MR**1484537**, 10.1016/S0246-0203(97)80109-4**6.**C. Liverani,*Flows, random perturbations and the rate of mixing*, Ergod. Th. and Dynam. Sys., to appear.**7.**Peter Walters,*Ruelle’s operator theorem and 𝑔-measures*, Trans. Amer. Math. Soc.**214**(1975), 375–387. MR**0412389**, 10.1090/S0002-9947-1975-0412389-8**8.**Peter Walters,*An introduction to ergodic theory*, Graduate Texts in Mathematics, vol. 79, Springer-Verlag, New York-Berlin, 1982. MR**648108****9.**A. Fisher and A. Lopes,*Polynomial decay of correlation and the central limit theorem for the equilibrium state of a non-Hölder potential*, Preprint.

Retrieve articles in *Transactions of the American Mathematical Society*
with MSC (1991):
58Fxx

Retrieve articles in all journals with MSC (1991): 58Fxx

Additional Information

**Mark Pollicott**

Affiliation:
Department of Mathematics, Manchester University, Oxford Road, Manchester M13 9PL, England

Email:
mp@ma.man.ac.uk

DOI:
https://doi.org/10.1090/S0002-9947-99-02382-X

Received by editor(s):
September 22, 1997

Published electronically:
September 17, 1999

Article copyright:
© Copyright 1999
American Mathematical Society