Entropy formula for random dynamical systems: relations between entropy, exponents and dimension

被引：9

作者：

Qian, M ^{[1
]}

Qian, MP ^{[1
]}

Xie, JS ^{[1
]}

机构：

[1] Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China

来源：

ERGODIC THEORY AND DYNAMICAL SYSTEMS | 2003年 / 23卷

关键词：

D O I：

10.1017/S0143385703000178

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we consider random dynamical systems generated by compositions of one-sided independent and identically distributed random diffeomorphisms of class C-2 on a compact manifold. We prove an entropy formula for such random dynamical systems without assuming the SRB condition. This result is the random version of the main result obtained by Ledrappier and Young (The metric entropy of diffeomorphisms. Part II: Relations between entropy, exponents and dimension. Ann. Math. 122 (1985), 540-574).

引用

页码：1907 / 1931

页数：25

共 50 条

[1] Entropy formula for endomorphisms: Relations between entropy, exponents and dimension
Qian, Min
Xie, Jian-Sheng
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2008, 21 (02) : 367 - 392
[2] THE METRIC ENTROPY OF DIFFEOMORPHISMS .2. RELATIONS BETWEEN ENTROPY, EXPONENTS AND DIMENSION
LEDRAPPIER, F
YOUNG, LS
ANNALS OF MATHEMATICS, 1985, 122 (03) : 540 - 574
[3] DIMENSION, ENTROPY AND LYAPUNOV EXPONENTS IN DIFFERENTIABLE DYNAMICAL-SYSTEMS
YOUNG, LS
PHYSICA A, 1984, 124 (1-3): : 639 - 645
[4] Katok's entropy formula of unstable metric entropy for random dynamical systems
Chen, Yexing
Cao, Yongluo
Zang, Yuntao
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2024, 531 (01)
[5] ENTROPY, LYAPUNOV EXPONENTS, AND HAUSDORFF DIMENSION IN DIFFERENTIABLE DYNAMICAL-SYSTEMS
YOUNG, LS
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS, 1983, 30 (08): : 599 - 607
[6] Entropy formula of Pesin type for noninvertible random dynamical systems
Pei–Dong Liu
Mathematische Zeitschrift, 1999, 230 : 201 - 239
[7] Entropy formula of Pesin type for noninvertible random dynamical systems
Liu, PD
MATHEMATISCHE ZEITSCHRIFT, 1999, 230 (02) : 201 - 239
[8] METASTABILITY, LYAPUNOV EXPONENTS, ESCAPE RATES, AND TOPOLOGICAL ENTROPY IN RANDOM DYNAMICAL SYSTEMS
Froyland, Gary
Stancevic, Ognjen
STOCHASTICS AND DYNAMICS, 2013, 13 (04)
[9] Entropy Production, Information Gain and Lyapunov Exponents of Random Hyperbolic Dynamical Systems
Jiang, Da-Quan
Qian, Min
Qian, Min-Ping
MATHEMATICAL THEORY OF NONEQUILIBRIUM STEADY STATES: ON THE FRONTIER OF PROBABILITY AND DYNAMICAL SYSTEMS, 2004, 1833 : 215 - 252
[10] Characterization of measures satisfying the Pesin entropy formula for random dynamical systems
Bahnmüller J.
Liu P.-D.
Journal of Dynamics and Differential Equations, 1998, 10 (3) : 425 - 448

← 1 2 3 4 5 →