Multifractal analysis of multiple ergodic averages

Aihua Fan; Jörg Schmeling; Meng Wu

doi:10.1016/j.crma.2011.08.014

Mathematical Analysis/Dynamical Systems

Multifractal analysis of multiple ergodic averages

Presented by: Jean-Pierre Kahane

Aihua Fan ¹; Jörg Schmeling ²; Meng Wu ¹

¹ LAMFA, UMR 6140 CNRS, Université de Picardie, 33, rue Saint Leu, 80039 Amiens, France
² MCMS, Lund Institute of Technology, Lund University, Box 118, 221 00 Lund, Sweden

Comptes Rendus. Mathématique, Volume 349 (2011) no. 17-18, pp. 961-964.

Abstract
Résumé

In this Note we present a complete solution to the problem of multifractal analysis of multiple ergodic averages in the case of symbolic dynamics for functions of two variables depending on the first coordinate.

Dans cette Note nous présentons une solution complète au problème de lʼanalyse multifractale des moyennes ergodiques multiples dans le cas du système dynamique symbolique pour les fonctions de deux variables dépendant de la première coordonnée.

Received: 2011-05-23
Accepted: 2011-08-18
Published online: 2011-09-01

DOI: 10.1016/j.crma.2011.08.014

Author's affiliations:

Aihua Fan ¹; Jörg Schmeling ²; Meng Wu ¹

¹ LAMFA, UMR 6140 CNRS, Université de Picardie, 33, rue Saint Leu, 80039 Amiens, France
² MCMS, Lund Institute of Technology, Lund University, Box 118, 221 00 Lund, Sweden

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     author = {Aihua Fan and J\"org Schmeling and Meng Wu},
     title = {Multifractal analysis of multiple ergodic averages},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {961--964},
     publisher = {Elsevier},
     volume = {349},
     number = {17-18},
     year = {2011},
     doi = {10.1016/j.crma.2011.08.014},
     language = {en},
}

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Aihua Fan; Jörg Schmeling; Meng Wu. Multifractal analysis of multiple ergodic averages. Comptes Rendus. Mathématique, Volume 349 (2011) no. 17-18, pp. 961-964. doi : 10.1016/j.crma.2011.08.014. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.08.014/

References
Cited by

[1] A.H. Fan Sur les dimension de mesures, Studia Math., Volume 111 (1994), pp. 1-17

[2] A.H. Fan, L.M. Liao, J.H. Ma, Level sets of multiple ergodic averages, preprint, 2009.

[3] A.H. Fan; L.M. Liao; J. Peyrière Generic points in systems of specification and Banach valued Birkhff ergodic average, DCDS, Volume 21 (2008), pp. 1103-1128

[4] A.H. Fan, J. Schmeling, M. Wu, Multiple ergodic averages and nonlinear transfer operators, preprint, 2011.

[5] R. Kenyon, Y. Peres, B. Solomyak, Hausdorff dimension for fractals invariant under the multiplicative integers, preprint, 2011.

[6] Y. Peres, B. Solomyak, Dimension spectrum for a nonconventional ergodic average, preprint, 2011.

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