no. 2
Unique ergodicity of asynchronous rotations, and application
Maucourant, François1
1Université de Rennes, IRMAR, Campus de Beaulieu, 35042 Rennes cedex (France)
Annales de l'Institut Fourier, Volume 76 (2026) no. 2, pp. 643-669

The main result of this paper is an analogue for a continuous family of tori of Kronecker–Weyl’s unique ergodicity of irrational rotations. We show that the notion corresponding in this setup to irrationality, namely asynchronicity, is satisfied in some homogeneous dynamical systems. This is used to prove the ergodicity of naturals lifts of invariant measures.

Nous étudions sur une famille continue de tores les rotations dites asynchrones, analogues aux rotations irrationnelles sur les tores classiques. Le résultat principal est l’unique ergodicité de ces rotations sur un monoïde adapté. Nous prouvons que la condition d’asynchronicité est vérifiée dans une famille d’exemples issue de la dynamique homogène, ce qui nous permet de déduire l’ergodicité de relevés de certaines transformations dans des fibrés en tores.

Received:
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Accepted:
Online First:
Published online:
DOI: 10.5802/aif.3718
Classification: 37A17
Keywords: unique ergodicity, homogeneous dynamics
Mots-clés : unique ergodicité, dynamique homogène

Maucourant, François  1

1 Université de Rennes, IRMAR, Campus de Beaulieu, 35042 Rennes cedex (France)
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Maucourant, François. Unique ergodicity of asynchronous rotations, and application. Annales de l'Institut Fourier, Volume 76 (2026) no. 2, pp. 643-669. doi: 10.5802/aif.3718

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