Almost reducibility of quasiperiodic SL(2, R)-cocycles in ultradifferentiable classes

被引：2

作者：

Chatal, Maxime ^{[1
]}

Chavaudret, Claire ^{[1
]}

机构：

[1] Univ Paris Cite, IMJ PRG, Paris, France

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2023年 / 356卷

关键词：

Quasi-periodic cocycles; Ultradifferentiable class; Almost reducibility; Brjuno-R?ssmann condition; Small divisors; KAM method; COCYCLES;

D O I：

10.1016/j.jde.2023.01.041

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given a quasiperiodic cocycle in sl(2, R) sufficiently close to a constant, we prove that it is almost reducible in ultradifferentiable class under an adapted arithmetic condition on the frequency vector.(c) 2023 Elsevier Inc. All rights reserved.

引用

页码：243 / 288

页数：46

共 15 条

[1]

Avila A, 2011, GEOM FUNCT ANAL, V21, P1001, DOI 10.1007/s00039-011-0135-6

[2]

Bounemoura A., 2019, Ann. Sc. Norm. Super. Pisa Cl. Sci., V19, P1

[3] REDUCIBILITY OF ULTRA-DIFFERENTIABLE QUASIPERIODIC COCYCLES UNDER AN ADAPTED ARITHMETIC CONDITION [J].

Bounemoura, Abed ;

Chavaudret, Claire ;

Liang, Shuqing .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2021, 149 (07) :2999-3012

[4]

Braun RW., 1990, Results in Mathematics, V17, P206, DOI [10.1007/BF03322459, DOI 10.1007/BF03322459]

[5] STRONG ALMOST REDUCIBILITY FOR ANALYTIC AND GEVREY QUASI-PERIODIC COCYCLES [J].

Chavaudret, Claire .

BULLETIN DE LA SOCIETE MATHEMATIQUE DE FRANCE, 2013, 141 (01) :47-106

[6] REDUCIBILITY OF QUASIPERIODIC COCYCLES UNDER A BRJUNO-RUSSMANN ARITHMETICAL CONDITION [J].

Chavaudret, Claire ;

Marmi, Stefano .

JOURNAL OF MODERN DYNAMICS, 2012, 6 (01) :59-78

[7] Reducibility of quasiperiodic cocycles in linear Lie groups [J].

Chavaudret, Claire .

ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2011, 31 :741-769

[8] A normal form theorem for Brjuno skew systems through renormalization [J].

Dias, Joao Lopes .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2006, 230 (01) :1-23

[9] Linearization of Gevrey flows on Td with a Brjuno type arithmetical condition [J].

Dias, Joao Lopes ;

Gaivao, Jose Pedro .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2019, 267 (12) :7167-7212

[10]

Eliasson L. H., 2001, Smooth Ergodic Theory and Its Applications, V69, P679

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