On random linear dynamical systems in a Banach space. I. Multiplicative Ergodic Theorem and Krein-Rutman type Theorems

被引：8

作者：

Lian, Zeng ^{[1
]}

Wang, Yi ^{[2
]}

机构：

[1] Sichuan Univ, Coll Math, Chengdu 610065, Sichuan, Peoples R China

[2] Univ Sci & Technol China, Sch Math Sci, Wu Wen Tsun Key Lab, Hefei 230026, Anhui, Peoples R China

来源：

ADVANCES IN MATHEMATICS | 2017年 / 312卷

关键词：

Random dynamical system; Banach space; Lyapunov exponents; Multiplicative ergodic theorem; Krein-Rutman Theorem; PRINCIPAL LYAPUNOV EXPONENTS; PARABOLIC EQUATIONS; FLOQUET BUNDLES; PRODUCTS; SEPARATION; FOLIATIONS; CONES;

D O I：

10.1016/j.aim.2017.03.024

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For linear random dynamical systems in a separable Banach space X, we derived a series of Krein-Rutman type Theorems with respect to co-invariant cone family with rank-k, which present a (quasi)-equivalence relation between the measurably co-invariant cone family and the measurably dominated splitting of X. Moreover, such (quasi)-equivalence relation turns out to be an equivalence relation whenever (i) k = 1; or (ii) in the frame of the Multiplicative Ergodic Theorem with certain Lyapunov exponent being greater than the negative infinity. For the second case, we thoroughly investigated the relations between the Lyapunov exponents, the co-invariant cone family and the measurably dominated splitting for linear random dynamical systems in X. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：374 / 424

页数：51