B. Host and B. Kra (2005) [5] have introduced the characteristic factors for studying “cubic ergodic means”. These factors allow one to resolve, in particular, multiple recurrence problems introduced by H. Furstenberg (1977) [4]. We show here that the continuity of the projection of the system in its characteristic factors characterises cubic means.
B. Host et B. Kra (2005) [5] introduisent des facteurs caractéristiques pour lʼétude de « moyennes ergodiques cubiques ». Ces facteurs permettent en particulier de résoudre des problèmes de récurrence multiple introduits par H. Furstenberg (1977) [4]. Nous allons montrer que la continuité de la projection du système dans ses facteurs caractéristiques caractérisent la convergence des moyennes cubiques.
Accepted:
Published online:
@article{CRMATH_2012__350_13-14_699_0, author = {Bertazzon, Jean-Fran\c{c}ois}, title = {Note sur la continuit\'e de la projection dans les facteurs de {Host{\textendash}Kra}}, journal = {Comptes Rendus. Math\'ematique}, pages = {699--702}, publisher = {Elsevier}, volume = {350}, number = {13-14}, year = {2012}, doi = {10.1016/j.crma.2012.08.006}, language = {fr}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2012.08.006/} }
TY - JOUR AU - Bertazzon, Jean-François TI - Note sur la continuité de la projection dans les facteurs de Host–Kra JO - Comptes Rendus. Mathématique PY - 2012 SP - 699 EP - 702 VL - 350 IS - 13-14 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2012.08.006/ DO - 10.1016/j.crma.2012.08.006 LA - fr ID - CRMATH_2012__350_13-14_699_0 ER -
%0 Journal Article %A Bertazzon, Jean-François %T Note sur la continuité de la projection dans les facteurs de Host–Kra %J Comptes Rendus. Mathématique %D 2012 %P 699-702 %V 350 %N 13-14 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2012.08.006/ %R 10.1016/j.crma.2012.08.006 %G fr %F CRMATH_2012__350_13-14_699_0
Bertazzon, Jean-François. Note sur la continuité de la projection dans les facteurs de Host–Kra. Comptes Rendus. Mathématique, Volume 350 (2012) no. 13-14, pp. 699-702. doi : 10.1016/j.crma.2012.08.006. http://archive.numdam.org/articles/10.1016/j.crma.2012.08.006/
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