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On hyperbolicity of close to piecewise constant linear cocycles over irrational rotations. / Ivanov, Alexey V. .

2022 Days on Diffraction (DD): Proceedings. Institute of Electrical and Electronics Engineers Inc., 2022. p. 63-69 9960970.

Research output: Chapter in Book/Report/Conference proceeding › Conference abstracts › Research › peer-review

Harvard

Ivanov, AV 2022, On hyperbolicity of close to piecewise constant linear cocycles over irrational rotations. in 2022 Days on Diffraction (DD): Proceedings., 9960970, Institute of Electrical and Electronics Engineers Inc., pp. 63-69, Days on Diffraction 2022, Санкт-Петербург, Russian Federation, 30/05/22. https://doi.org/10.1109/DD55230.2022.9960970

APA

Ivanov, A. V. (2022). On hyperbolicity of close to piecewise constant linear cocycles over irrational rotations. In 2022 Days on Diffraction (DD): Proceedings (pp. 63-69). [9960970] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/DD55230.2022.9960970

Vancouver

Ivanov AV. On hyperbolicity of close to piecewise constant linear cocycles over irrational rotations. In 2022 Days on Diffraction (DD): Proceedings. Institute of Electrical and Electronics Engineers Inc. 2022. p. 63-69. 9960970 https://doi.org/10.1109/DD55230.2022.9960970

Author

Ivanov, Alexey V. . / On hyperbolicity of close to piecewise constant linear cocycles over irrational rotations. 2022 Days on Diffraction (DD): Proceedings. Institute of Electrical and Electronics Engineers Inc., 2022. pp. 63-69

BibTeX

@inbook{db588ff74bf643a0b19ce9e40b39bdb6,
title = "On hyperbolicity of close to piecewise constant linear cocycles over irrational rotations",
abstract = "We study a family of skew products FA,t = (σω, At)over irrational rotation σω(x) = x + ω of a circleT1, which depend on a real parameter t. It is supposed that the transformation At ∈ C(T1, SL(2,R))is of the form At(x) = R(ϕ(x))Z(λ(x)), where R(ϕ)stands for a rotation in R2 over an angle ϕ andZ(λ) = diag{λ, λ−1} is a diagonal matrix. Assuming λ(x) ≥ λ0 1 and the function ϕ to be piecewise linear such that cos(x) possesses only simplezeroes, we study the problem of uniform hyperbolicity for the cocycle generated by FA,t. We applythe critical set method to formulate sufficient conditions on the parameter values which guarantee theuniform hyperbolicity of the cocycle. Application tothe Schr¨odinger cocycles is also discussed.",
author = "Ivanov, {Alexey V.}",
year = "2022",
doi = "10.1109/DD55230.2022.9960970",
language = "English",
pages = "63--69",
booktitle = "2022 Days on Diffraction (DD)",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
address = "United States",
note = "null ; Conference date: 30-05-2022 Through 03-06-2022",
url = "http://www.pdmi.ras.ru/~dd/",

}

RIS

TY - CHAP

T1 - On hyperbolicity of close to piecewise constant linear cocycles over irrational rotations

AU - Ivanov, Alexey V.

PY - 2022

Y1 - 2022

N2 - We study a family of skew products FA,t = (σω, At)over irrational rotation σω(x) = x + ω of a circleT1, which depend on a real parameter t. It is supposed that the transformation At ∈ C(T1, SL(2,R))is of the form At(x) = R(ϕ(x))Z(λ(x)), where R(ϕ)stands for a rotation in R2 over an angle ϕ andZ(λ) = diag{λ, λ−1} is a diagonal matrix. Assuming λ(x) ≥ λ0 1 and the function ϕ to be piecewise linear such that cos(x) possesses only simplezeroes, we study the problem of uniform hyperbolicity for the cocycle generated by FA,t. We applythe critical set method to formulate sufficient conditions on the parameter values which guarantee theuniform hyperbolicity of the cocycle. Application tothe Schr¨odinger cocycles is also discussed.

AB - We study a family of skew products FA,t = (σω, At)over irrational rotation σω(x) = x + ω of a circleT1, which depend on a real parameter t. It is supposed that the transformation At ∈ C(T1, SL(2,R))is of the form At(x) = R(ϕ(x))Z(λ(x)), where R(ϕ)stands for a rotation in R2 over an angle ϕ andZ(λ) = diag{λ, λ−1} is a diagonal matrix. Assuming λ(x) ≥ λ0 1 and the function ϕ to be piecewise linear such that cos(x) possesses only simplezeroes, we study the problem of uniform hyperbolicity for the cocycle generated by FA,t. We applythe critical set method to formulate sufficient conditions on the parameter values which guarantee theuniform hyperbolicity of the cocycle. Application tothe Schr¨odinger cocycles is also discussed.

U2 - 10.1109/DD55230.2022.9960970

DO - 10.1109/DD55230.2022.9960970

M3 - Conference abstracts

SP - 63

EP - 69

BT - 2022 Days on Diffraction (DD)

PB - Institute of Electrical and Electronics Engineers Inc.

Y2 - 30 May 2022 through 3 June 2022

ER -

ID: 103386416