Analyticity of the Lyapunov exponents of random products of quasi-periodic cocycles

被引：0

作者：

Bezerra, Jamerson ^{[3
]}

Sanchez, Adriana ^{[1
]}

Tall, El Hadji Yaya ^{[2
]}

机构：

[1] Univ Costa Rica, Ctr Invest Matemat Pura & Aplicada Escuela Matemat, San Jose, Costa Rica

[2] Univ Sao Paulo, Inst Matemat & Estat, Sao Paulo, Brazil

[3] Nicolaus Copernicus Univ, Fac Math & Comp Sci, Ul Chopina 12-18, PL-87100 Torun, Poland

来源：

NONLINEARITY | 2023年 / 36卷 / 06期

基金：

巴西圣保罗研究基金会;

关键词：

skew product; quasi-periodic cocycles; random product; Lyapunov exponents; CONTINUITY;

D O I：

10.1088/1361-6544/acd299

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that the top Lyapunov exponent ?(+)(p) , p = (p(1), . . . ,p(N)) with p(i) > 0 for each i, associated with a random product of quasi-periodic cocycles depends real analytically on the transition probabilities p whenever ?(+)(p) is simple. Moreover if the spectrum at p is simple (all Lyapunov exponents having multiplicity one ) then all Lyapunov exponents depend real analytically on p.

引用

页码：3467 / 3482

页数：16

共 27 条

[11] Mixed Random-Quasiperiodic Cocycles [J].

Cai, Ao ;

Duarte, Pedro ;

Klein, Silvius .

BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, 2022, 53 (04) :1469-1497

[12]

Damanik D, 2007, P SYMP PURE MATH, V76, P539

[13] Schrodinger operators with dynamically defined potentials [J].

Damanik, David .

ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2017, 37 :1681-1764

[14]

Duarte P., 2016, Atlantis Studies in Dynamical Systems, V3, DOI DOI 10.2991/978-94-6239-124-6

[15] Continuity, positivity and simplicity of the Lyapunov exponents for quasi-periodic cocycles [J].

Duarte, Pedro ;

Klein, Silvius .

JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2019, 21 (07) :2051-2106

[16] A RANDOM COCYCLE WITH NON HOLDER LYAPUNOV EXPONENT [J].

Duarte, Pedro ;

Klein, Silvius ;

Santos, Manuel .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2019, 39 (08) :4841-4861

[17] RANDOM MATRIX PRODUCTS AND MEASURES ON PROJECTIVE SPACES [J].

FURSTENBERG, H ;

KIFER, Y .

ISRAEL JOURNAL OF MATHEMATICS, 1983, 46 (1-2) :12-32

[18] PRODUCTS OF RANDOM MATRICES [J].

FURSTENBERG, H ;

KESTEN, H .

ANNALS OF MATHEMATICAL STATISTICS, 1960, 31 (02) :457-469

[19]

Furstenberg H., 1963, Trans. Amer. Math. Soc., V108, P377, DOI [10.1090/S0002-9947-1963-0163345-0, DOI 10.1090/S0002-9947-1963-0163345-0]

[20] LARGE NUMBER LAW AND PERTURBATIONS FOR REDUCIBLE PRODUCTS OF INDEPENDENT ALEATORY MATRICES [J].

HENNION, H .

ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE, 1984, 67 (03) :265-278

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