PERIODIC APPROXIMATION OF EXCEPTIONAL LYAPUNOV EXPONENTS FOR SEMI-INVERTIBLE OPERATOR COCYCLES

被引：15

作者：

Backes, Lucas ^{[1
]}

Dragicevic, Davor ^{[2
]}

机构：

[1] Univ Fed Rio Grande do Sul, Dept Matemat, Av Bento Goncalves 9500, BR-91509900 Porto Alegre, RS, Brazil

[2] Univ Rijeka, Dept Math, Rijeka 51000, Croatia

来源：

ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA | 2019年 / 44卷

关键词：

Semi-invertible operator cocycles; Lyapunov exponents; periodic points; approximation; GROWTH-RATES; THEOREM; MANIFOLDS; ENTROPY;

D O I：

10.5186/aasfm.2019.4410

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that for semi-invertible and Holder continuous linear cocycles A acting on an arbitrary Banach space and defined over a base space that satisfies the Anosov closing property, all exceptional Lyapunov exponents of A with respect to an ergodic invariant measure for base dynamics can be approximated with Lyapunov exponents of A with respect to ergodic measures supported on periodic orbits. Our result is applicable to a wide class of infinite-dimensional dynamical systems.

引用

页码：183 / 209

页数：27

共 29 条

[1]

[Anonymous], 2014, LECT LYAPUNOV EXPONE

[2]

[Anonymous], 2007, ENCY MATH ITS APPL

[3]

ARNOLD L., 1998, Monographs in Mathematics

[4] ON THE PERIODIC APPROXIMATION OF LYAPUNOV EXPONENTS FOR SEMI-INVERTIBLE COCYCLES [J].

Backes, Lucas .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2017, 37 (12) :6353-6368

[5] Entropy, volume growth and SRB measures for Banach space mappings [J].

Blumenthal, Alex ;

Young, Lai-Sang .

INVENTIONES MATHEMATICAE, 2017, 207 (02) :833-893

[6] A VOLUME-BASED APPROACH TO THE MULTIPLICATIVE ERGODIC THEOREM ON BANACH SPACES [J].

Blumenthal, Alex .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2016, 36 (05) :2377-2403

[7] Non-zero Lyapunov exponents and uniform hyperbolicity [J].

Cao, YL .

NONLINEARITY, 2003, 16 (04) :1473-1479

[8] On growth rates of sub-additive functions for semi-flows: Determined and random cases [J].

Cao, Yongluo .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2006, 231 (01) :1-17

[9] A Spectral Approach for Quenched Limit Theorems for Random Expanding Dynamical Systems [J].

Dragicevic, Davor ;

Froyland, G. ;

Gonzalez-Tokman, C. ;

Vaienti, S. .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2018, 360 (03) :1121-1187

[10] Holder continuity of Oseledets splittings for semi-invertible operator cocycles [J].

Dragicevic, Davor ;

Froyland, Gary .

ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2018, 38 :961-981

← 1 2 3 →