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On linear cocycles over irrational rotations with secondary collisions. / Ivanov, Alexey V.

Proceedings of the International Conference Days on Diffraction 2021, DD 2021. 2021. p. 81-86.

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

Harvard

Ivanov, AV 2021, On linear cocycles over irrational rotations with secondary collisions. in Proceedings of the International Conference Days on Diffraction 2021, DD 2021. pp. 81-86. https://doi.org/10.1109/DD52349.2021.9598487

APA

Ivanov, A. V. (2021). On linear cocycles over irrational rotations with secondary collisions. In Proceedings of the International Conference Days on Diffraction 2021, DD 2021 (pp. 81-86) https://doi.org/10.1109/DD52349.2021.9598487

Vancouver

Ivanov AV. On linear cocycles over irrational rotations with secondary collisions. In Proceedings of the International Conference Days on Diffraction 2021, DD 2021. 2021. p. 81-86 https://doi.org/10.1109/DD52349.2021.9598487

Author

Ivanov, Alexey V. / On linear cocycles over irrational rotations with secondary collisions. Proceedings of the International Conference Days on Diffraction 2021, DD 2021. 2021. pp. 81-86

BibTeX

@inproceedings{00970fa97f9048ba881364d5847f971c,
title = "On linear cocycles over irrational rotations with secondary collisions",
abstract = "We consider a skew product FA = (s?,A) over irrational rotation {\sigma \omega }(x) = x + \omega of a circle {\mathbb{T}1}. It is supposed that the transformation A:{\mathbb{T}1} \to SL(2,\mathbb{R}), being a C2-map, has the form A(x) = R(\varphi (x))Z(\lambda (x)), where R() is a rotation in 2 over the angle and Z(?) = diag{?,?-1} is a diagonal matrix. Assuming that ?(x) =?0 > 1 with a sufficiently large constant ?o and the function is such that cos (x) possesses only simple zeroes, we study hyperbolic properties of the cocycle generated by FA. We apply the critical set method to show that, under some additional requirements on the derivative of the function , the secondary collisions compensate weakening of the hyperbolicity due to primary collisions and the cocycle generated by FA becomes hyperbolic in contrary to the case when secondary collisions can be partially eliminated.",
author = "Ivanov, {Alexey V.}",
year = "2021",
month = jan,
day = "1",
doi = "10.1109/DD52349.2021.9598487",
language = "English",
pages = "81--86",
booktitle = "Proceedings of the International Conference Days on Diffraction 2021, DD 2021",

}

RIS

TY - GEN

T1 - On linear cocycles over irrational rotations with secondary collisions

AU - Ivanov, Alexey V.

PY - 2021/1/1

Y1 - 2021/1/1

N2 - We consider a skew product FA = (s?,A) over irrational rotation {\sigma \omega }(x) = x + \omega of a circle {\mathbb{T}1}. It is supposed that the transformation A:{\mathbb{T}1} \to SL(2,\mathbb{R}), being a C2-map, has the form A(x) = R(\varphi (x))Z(\lambda (x)), where R() is a rotation in 2 over the angle and Z(?) = diag{?,?-1} is a diagonal matrix. Assuming that ?(x) =?0 > 1 with a sufficiently large constant ?o and the function is such that cos (x) possesses only simple zeroes, we study hyperbolic properties of the cocycle generated by FA. We apply the critical set method to show that, under some additional requirements on the derivative of the function , the secondary collisions compensate weakening of the hyperbolicity due to primary collisions and the cocycle generated by FA becomes hyperbolic in contrary to the case when secondary collisions can be partially eliminated.

AB - We consider a skew product FA = (s?,A) over irrational rotation {\sigma \omega }(x) = x + \omega of a circle {\mathbb{T}1}. It is supposed that the transformation A:{\mathbb{T}1} \to SL(2,\mathbb{R}), being a C2-map, has the form A(x) = R(\varphi (x))Z(\lambda (x)), where R() is a rotation in 2 over the angle and Z(?) = diag{?,?-1} is a diagonal matrix. Assuming that ?(x) =?0 > 1 with a sufficiently large constant ?o and the function is such that cos (x) possesses only simple zeroes, we study hyperbolic properties of the cocycle generated by FA. We apply the critical set method to show that, under some additional requirements on the derivative of the function , the secondary collisions compensate weakening of the hyperbolicity due to primary collisions and the cocycle generated by FA becomes hyperbolic in contrary to the case when secondary collisions can be partially eliminated.

UR - http://www.scopus.com/inward/record.url?scp=85123289854&partnerID=8YFLogxK

U2 - 10.1109/DD52349.2021.9598487

DO - 10.1109/DD52349.2021.9598487

M3 - Conference contribution

AN - SCOPUS:85123289854

SP - 81

EP - 86

BT - Proceedings of the International Conference Days on Diffraction 2021, DD 2021

ER -

ID: 95584618