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Trudy Moskovskogo Matematicheskogo Obshchestva, 2021, Volume 82, Issue 1, Pages 185–203 (Mi mmo654)  
This article is cited in 2 scientific papers (total in 2 papers)

A note on double rotations of infinite type

M. Artigiania, Ch. Fougeronb, P. Hubertc, A. Skripchenkode

a School of Engineering, Science and Technology, Universidad del Rosario, Bogotá 111711, Colombia
b Research Institute on the Foundations of Computer Science
c Institut de Mathématiques de Marseille
d National Research University Higher School of Economics, Moscow
e Russia Skolkovo Institute for Science and Technology, Skolkovo Innovation Center, Moscow, Russia
Full-text PDF (275 kB) Citations (2)
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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.
Key words and phrases: interval translation mappings, unique ergodicity, Rauzy induction.
Funding agency Grant number
Russian Science Foundation 20-41-09009
A. Skripchenko appreciates the support of RSF-ANR Grant, Project 20-41-09009.
Received: 23.02.2021
English version:
Transactions of the Moscow Mathematical Society, 2021, Volume 82, Pages 157–172
DOI: https://doi.org/10.1090/mosc/311
Bibliographic databases:
Document Type: Article
UDC: 517.938
MSC: 37E05
Language: English
Citation: M. Artigiani, Ch. Fougeron, P. Hubert, A. Skripchenko, “A note on double rotations of infinite type”, Tr. Mosk. Mat. Obs., 82, no. 1, MCCME, M., 2021, 185–203; Trans. Moscow Math. Soc., 82 (2021), 157–172
Citation in format AMSBIB
\Bibitem{ArtFouHub21}
\by M.~Artigiani, Ch.~Fougeron, P.~Hubert, A.~Skripchenko
\paper A note on double rotations of infinite type
\serial Tr. Mosk. Mat. Obs.
\yr 2021
\vol 82
\issue 1
\pages 185--203
\publ MCCME
\publaddr M.
\mathnet{http://mi.mathnet.ru/mmo654}
\transl
\jour Trans. Moscow Math. Soc.
\yr 2021
\vol 82
\pages 157--172
\crossref{https://doi.org/10.1090/mosc/311}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85127460428}
Linking options:
  • https://www.mathnet.ru/eng/mmo654
  • https://www.mathnet.ru/eng/mmo/v82/i1/p185
    • This publication is cited in the following 2 articles:
    1. A. S. Skripchenko, “Renormalization in one-dimensional dynamics”, Russian Math. Surveys, 78:6 (2023), 983–1021  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. Sergey Kryzhevich, Viktor Avrutin, Nikita Begun, Dmitrii Rachinskii, Khosro Tajbakhsh, “Dynamics of Systems with a Discontinuous Hysteresis Operator and Interval Translation Maps”, Axioms, 10:2 (2021), 80  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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    		Trudy Moskovskogo Matematicheskogo Obshchestva
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