A note on double rotations of infinite type

M. Artigiani; C. Fougeron; P. Hubert; A. Skripchenko

doi:10.1090/mosc/311

A note on double rotations of infinite type

M. Artigiani
, C. Fougeron
, P. Hubert
, A. Skripchenko

urosario

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

6 Scopus citations

Abstract

We introduce a new renormalization procedure on double rotations, which is reminiscent of the classical Rauzy induction. Using this renormalization we prove that the set of parameters which induce infinite type double rotations has Hausdorff dimension strictly smaller than 3. Moreover, we construct a natural invariant measure supported on these parameters and show that, with respect to this measure, almost all double rotations are uniquely ergodic.

Original language	English (US)
Pages (from-to)	157-172
Number of pages	16
Journal	Transactions of the Moscow Mathematical Society
Volume	82
Issue number	1
DOIs	https://doi.org/10.1090/mosc/311
State	Published - 2021

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SDG 1 No Poverty

All Science Journal Classification (ASJC) codes

Mathematics (miscellaneous)

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10.1090/mosc/311

Cite this

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title = "A note on double rotations of infinite type",

abstract = "We introduce a new renormalization procedure on double rotations, which is reminiscent of the classical Rauzy induction. Using this renormalization we prove that the set of parameters which induce infinite type double rotations has Hausdorff dimension strictly smaller than 3. Moreover, we construct a natural invariant measure supported on these parameters and show that, with respect to this measure, almost all double rotations are uniquely ergodic.",

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T1 - A note on double rotations of infinite type

AU - Artigiani, M.

AU - Fougeron, C.

AU - Hubert, P.

AU - Skripchenko, A.

PY - 2021

Y1 - 2021

N2 - We introduce a new renormalization procedure on double rotations, which is reminiscent of the classical Rauzy induction. Using this renormalization we prove that the set of parameters which induce infinite type double rotations has Hausdorff dimension strictly smaller than 3. Moreover, we construct a natural invariant measure supported on these parameters and show that, with respect to this measure, almost all double rotations are uniquely ergodic.

AB - We introduce a new renormalization procedure on double rotations, which is reminiscent of the classical Rauzy induction. Using this renormalization we prove that the set of parameters which induce infinite type double rotations has Hausdorff dimension strictly smaller than 3. Moreover, we construct a natural invariant measure supported on these parameters and show that, with respect to this measure, almost all double rotations are uniquely ergodic.

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UR - https://www.scopus.com/pages/publications/85127460428#tab=citedBy

U2 - 10.1090/mosc/311

DO - 10.1090/mosc/311

M3 - Research Article

AN - SCOPUS:85127460428

SN - 0077-1554

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SP - 157

EP - 172

JO - Transactions of the Moscow Mathematical Society

JF - Transactions of the Moscow Mathematical Society

IS - 1

ER -

A note on double rotations of infinite type

Abstract

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