A Kam Scheme for SL(2, ℝ) Cocycles with Liouvillean Frequencies

Artur Avila; Bassam Fayad; Raphaël Krikorian

doi:10.1007/s00039-011-0135-6

A Kam Scheme for SL(2, ℝ) Cocycles with Liouvillean Frequencies

Artur Avila
, Bassam Fayad
, Raphaël Krikorian

Research output: Contribution to journal › Article › peer-review

Abstract

We develop a new KAM scheme that applies to SL(2, ℝ) cocycles with one frequency, irrespective of any Diophantine condition on the base dynamics. It gives a generalization of Dinaburg-Sinai's theorem to arbitrary frequencies: under a closeness to constant assumption, the non-Abelian part of the classical reducibility problem can always be solved for a positive measure set of parameters.

Original language	English
Pages (from-to)	1001-1019
Number of pages	19
Journal	Geometric and Functional Analysis
Volume	21
Issue number	5
DOIs	https://doi.org/10.1007/s00039-011-0135-6
Publication status	Published - 1 Oct 2011

Keywords

Quasiperiodic cocycles
ergodic Schrödinger operators
reducibility

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10.1007/s00039-011-0135-6

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title = "A Kam Scheme for SL(2, ℝ) Cocycles with Liouvillean Frequencies",

abstract = "We develop a new KAM scheme that applies to SL(2, ℝ) cocycles with one frequency, irrespective of any Diophantine condition on the base dynamics. It gives a generalization of Dinaburg-Sinai's theorem to arbitrary frequencies: under a closeness to constant assumption, the non-Abelian part of the classical reducibility problem can always be solved for a positive measure set of parameters.",

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AU - Avila, Artur

AU - Fayad, Bassam

AU - Krikorian, Raphaël

PY - 2011/10/1

Y1 - 2011/10/1

N2 - We develop a new KAM scheme that applies to SL(2, ℝ) cocycles with one frequency, irrespective of any Diophantine condition on the base dynamics. It gives a generalization of Dinaburg-Sinai's theorem to arbitrary frequencies: under a closeness to constant assumption, the non-Abelian part of the classical reducibility problem can always be solved for a positive measure set of parameters.

AB - We develop a new KAM scheme that applies to SL(2, ℝ) cocycles with one frequency, irrespective of any Diophantine condition on the base dynamics. It gives a generalization of Dinaburg-Sinai's theorem to arbitrary frequencies: under a closeness to constant assumption, the non-Abelian part of the classical reducibility problem can always be solved for a positive measure set of parameters.

KW - Quasiperiodic cocycles

KW - ergodic Schrödinger operators

KW - reducibility

U2 - 10.1007/s00039-011-0135-6

DO - 10.1007/s00039-011-0135-6

M3 - Article

AN - SCOPUS:80053600619

SN - 1016-443X

VL - 21

SP - 1001

EP - 1019

JO - Geometric and Functional Analysis

JF - Geometric and Functional Analysis

IS - 5

ER -

A Kam Scheme for SL(2, ℝ) Cocycles with Liouvillean Frequencies

Abstract

Keywords

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