[Les moyennes ergodiques des produits cartésiens des flots paraboliques]
We consider a direct product of a suspension flow over a substitution dynamical system and an arbitrary ergodic flow and give quantitative estimates for the speed of convergence for ergodic integrals of such systems. Our argument relies on new uniform estimates of the spectral measure for suspension flows over substitution dynamical systems. The paper answers a question by Jon Chaika.
Pour le produit cartésien d’un flot ergodique arbitraire avec un flot de suspension sur un système de substitution, nous estimons la vitesse de convergence des intégrales ergodiques. Notre argument se base sur les bornes uniformes pour les mesures spectrales des flots de suspension sur les systèmes de substitution. Notre résultat répond à une question de Jon Chaika.
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Accepté le :
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DOI : 10.24033/bsmf.2770
Keywords: Substitution dynamical system, spectral measure, Hölder continuity
Mots-clés : Système de substitution, mesure spectrale, continuité de Hölder
Bufetov, Alexander I. 1 ; Solomyak, Boris 2
@article{BSMF_2018__146_4_675_0,
author = {Bufetov, Alexander I. and Solomyak, Boris},
title = {On ergodic averages for parabolic product flows},
journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
pages = {675--690},
year = {2018},
publisher = {Soci\'et\'e math\'ematique de France},
volume = {146},
number = {4},
doi = {10.24033/bsmf.2770},
mrnumber = {3936539},
zbl = {1414.37001},
language = {en},
url = {https://www.numdam.org/articles/10.24033/bsmf.2770/}
}
TY - JOUR AU - Bufetov, Alexander I. AU - Solomyak, Boris TI - On ergodic averages for parabolic product flows JO - Bulletin de la Société Mathématique de France PY - 2018 SP - 675 EP - 690 VL - 146 IS - 4 PB - Société mathématique de France UR - https://www.numdam.org/articles/10.24033/bsmf.2770/ DO - 10.24033/bsmf.2770 LA - en ID - BSMF_2018__146_4_675_0 ER -
%0 Journal Article %A Bufetov, Alexander I. %A Solomyak, Boris %T On ergodic averages for parabolic product flows %J Bulletin de la Société Mathématique de France %D 2018 %P 675-690 %V 146 %N 4 %I Société mathématique de France %U https://www.numdam.org/articles/10.24033/bsmf.2770/ %R 10.24033/bsmf.2770 %G en %F BSMF_2018__146_4_675_0
Bufetov, Alexander I.; Solomyak, Boris. On ergodic averages for parabolic product flows. Bulletin de la Société Mathématique de France, Tome 146 (2018) no. 4, pp. 675-690. doi: 10.24033/bsmf.2770
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