LIMIT-THEOREMS AND MARKOV APPROXIMATIONS FOR CHAOTIC DYNAMICAL-SYSTEMS

被引：78

作者：

CHERNOV, NI

机构：

[1] Department of Mathematics, University of Alabama at Birmingham, Birmingham, 35294, AL

来源：

PROBABILITY THEORY AND RELATED FIELDS | 1995年 / 101卷 / 03期

关键词：

D O I：

10.1007/BF01200500

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We prove the central limit theorem and weak invariance principle for abstract dynamical systems based on bounds on their mixing coefficients. We also develop techniques of Markov approximations for dynamical systems. We apply our results to expanding interval maps, Axiom A diffeomorphisms, chaotic billiards and hyperbolic attractors.

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页码：321 / 362

页数：42

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[1] ENTROPY A COMPLETE METRIC INVARIANT FOR AUTOMORPHISMS OF TORUS [J].

ADLER, RL ;

WEISS, B .

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1967, 57 (06) :1573-+

[2]

AFRUIMOVICH VS, 1995, IN PRESS CHAOS ZAOC, V5

[3]

[Anonymous], 1970, RUSS MATH SURV, DOI [10.1070/RM1970v025n02ABEH003794, DOI 10.1070/RM1970V025N02ABEH003794]

[4]

Billingsley P, 1968, CONVERGENCE PROBABIL

[5]

Bowen R., 1975, LECT NOTES MATH, V470

[6] ON THE CENTRAL LIMIT QUESTION UNDER ABSOLUTE REGULARITY [J].

BRADLEY, RC .

ANNALS OF PROBABILITY, 1985, 13 (04) :1314-1325

[7] STATISTICAL PROPERTIES OF 2-DIMENSIONAL HYPERBOLIC BILLIARDS [J].

BUNIMOVICH, LA ;

SINAI, YG ;

CHERNOV, NI .

RUSSIAN MATHEMATICAL SURVEYS, 1991, 46 (04) :47-106

[8] STATISTICAL PROPERTIES OF LORENTZ GAS WITH PERIODIC CONFIGURATION OF SCATTERERS [J].

BUNIMOVICH, LA ;

SINAI, YG .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1981, 78 (04) :479-497

[9] MARKOV PARTITIONS FOR 2-DIMENSIONAL HYPERBOLIC BILLIARDS [J].

BUNIMOVICH, LA ;

SINAI, YG ;

CHERNOV, NI .

RUSSIAN MATHEMATICAL SURVEYS, 1990, 45 (03) :105-152

[10] CORRECTION [J].

BUNIMOVICH, LA .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1986, 107 (02) :357-358

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