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.
Accepted:
Published online:
Aihua Fan 1; Jörg Schmeling 2; Meng Wu 1
@article{CRMATH_2011__349_17-18_961_0, 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}, }
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/
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[2] A.H. Fan, L.M. Liao, J.H. Ma, Level sets of multiple ergodic averages, preprint, 2009.
[3] 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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