NON-UNIFORMLY EXPANDING DYNAMICAL SYSTEMS: MULTI-DIMENSION

被引：2

作者：

Ye, Yuan-Ling ^{[1
]}

机构：

[1] South China Normal Univ, Sch Math Sci, Guangzhou 510631, Guangdong, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2019年 / 39卷 / 05期

关键词：

Non-uniformly expanding dynamical system; Adler's condition; Perron-Frobenius operator; invariant measure; invariant density; INVARIANT-MEASURES; MULTIDIMENSIONAL MAPS; LARGE DEVIATIONS; RUELLE OPERATOR; SBR MEASURES; INDIFFERENT; DECAY; TRANSFORMATIONS; EXISTENCE; RATES;

D O I：

10.3934/dcds.2019106

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Dynamical systems on the interval [0, 1], satisfying the Thaler's condition, have been extensively studied. In this paper we consider invariant density and statistical properties of non-uniformly expanding dynamical systems on R-d (d >= 1). We present a critical regular condition that is a supplement and a development of the Thaler's condition, and it is very closely related to Lamperti's criterion. Under this new condition, we offer a method for studying the dynamical systems. A continuity description of the invariant density is presented; and a convergence theorem for iterations of Perron-Frobenius operator is set up. Furthermore, we establish a more exact result for one-dimensional systems.

引用

页码：2511 / 2553

页数：43

共 35 条

[1] Aaronson J., 1997, An Introduction to Infinite Ergodic Theory
[2] [Anonymous], 1958, Trans. Am. Math. Soc, DOI DOI 10.1090/S0002-9947-1958-0094863-X
[3] Baladi V., 2000, Positive Transfer Operators and Decay of Correlations, V16
[4] Bowen R, 2008, LECT NOTES MATH, V470, P1, DOI 10.1007/978-3-540-77695-6
[5] INVARIANT MEASURES FOR MARKOV MAPS OF THE INTERVAL
BOWEN, R
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1979, 69 (01) : 1 - 17
[6] Dunford N., 1958, Linear Operators. Part I General Theory
[7] Gouëzel S, 2006, B SOC MATH FR, V134, P1
[8] CORRELATION ASYMPTOTICS FROM LARGE DEVIATIONS IN DYNAMICAL SYSTEMS WITH INFINITE MEASURE
Gouezel, Sebastien
[J]. COLLOQUIUM MATHEMATICUM, 2011, 125 (02) : 193 - 212
[9] Slowly mixing systems and intermittency maps
Holland, M
[J]. ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2005, 25 : 133 - 159
[10] Absolutely continuous invariant measures for non-uniformly expanding maps
Hu, Huyi
Vaienti, Sandro
[J]. ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2009, 29 : 1185 - 1215

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