NEW DEVELOPMENTS IN THE ERGODIC-THEORY OF NONLINEAR DYNAMICAL-SYSTEMS

被引:3
作者
BENEDICKS, M
机构
来源
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 1994年 / 346卷 / 1679期
关键词
D O I
10.1098/rsta.1994.0015
中图分类号
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号
07 ; 0710 ; 09 ;
摘要
The purpose of this paper is to give a survey of recent results on non-uniformly hyperbolic dynamical systems. The emphasis is on the existence of strange attractors and Sinai-Ruelle-Bowen measures for Henon maps, but we also describe results about statistical properties of such dynamical systems and state some of the open questions in this area.
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页码:145 / 157
页数:13
相关论文
共 28 条
[1]   ABSOLUTELY CONTINUOUS INVARIANT-MEASURES AND RANDOM PERTURBATIONS FOR CERTAIN ONE-DIMENSIONAL MAPS [J].
BENEDICKS, M ;
YOUNG, LS .
ERGODIC THEORY AND DYNAMICAL SYSTEMS, 1992, 12 :13-37
[2]   ON ITERATIONS OF 1 - AX-2 ON ( - 1, 1) [J].
BENEDICKS, M ;
CARLESON, L .
ANNALS OF MATHEMATICS, 1985, 122 (01) :1-25
[3]   THE DYNAMICS OF THE HENON MAP [J].
BENEDICKS, M ;
CARLESON, L .
ANNALS OF MATHEMATICS, 1991, 133 (01) :73-169
[4]   SINAI-BOWEN-RUELLE MEASURES FOR CERTAIN HENON MAPS [J].
BENEDICKS, M ;
YOUNG, LS .
INVENTIONES MATHEMATICAE, 1993, 112 (03) :541-576
[5]  
CARLESON L, 1990, 1990 P INT C MATH KY, V2, P1241
[6]  
DUARTE P, 1993, PLENTY ELLIPTIC ISLA
[7]   ERGODIC-THEORY OF CHAOS AND STRANGE ATTRACTORS [J].
ECKMANN, JP ;
RUELLE, D .
REVIEWS OF MODERN PHYSICS, 1985, 57 (03) :617-656
[8]  
FATHI A, 1983, LECT NOTES MATH, V1007, P177
[9]  
Guckenheimer J., 1979, PUBL MATH-PARIS, V50, P307
[10]   2-DIMENSIONAL MAPPING WITH A STRANGE ATTRACTOR [J].
HENON, M .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1976, 50 (01) :69-77