By J. Besineau (auth.), Prof. Gérard Rauzy (eds.)
Read or Download Répartition Modulo 1: Actes du Colloque de Marseille-Luminy, 4 au 7 Juin 1974 PDF
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Extra resources for Répartition Modulo 1: Actes du Colloque de Marseille-Luminy, 4 au 7 Juin 1974
Example text
Art, Jl vient est done n6cessairement, D'apr~s la d~finition 3, T~.. -r~. i pour Ic groupe engendr~ par T~. ~ur u. '1~:~ sonL les groupes de t r a n s l a t i o n s . Les exempleg prls au paragraphe 1 . ~t3on. ~O+~.. , ~TN) est une suite pour laquelle le syst~me d'int6gralcs est presque invariant pour le groupe engendr~ par 9 dans T . 2 - Une majoration de l'erreur Soit ~) unz suite ~quir6partie sur un sous-groupe To du groupe com- pact ab~lien T . Salt S _ la projection sur le sous-espaee ~(~/~)C'~) ici de donner une majoration de "l'erreur" ~ - - 5 ~ .
Ou ~-I 9 Ainsl, les points 51 ne laissent pas d'intervalles fibres sup~rleurs en iongueur ~ ~ . 4 ~ . ,81[. )~ T est ~ordonoante de &~) ; on a -- -(= + ~r . pou~ = ~ I19~,,~1/ pros 9 ~-, e. partl- Z. ers J r % ~~176'~ ~ est ~rratlonno,, o'est-~-d~re s i tend vers l'infini. Si ~ est rationnel au contralre, ~ . ~ ~aut J ~ # . o~ ~. ,~,'~ par Dans co d e r n i e r cas, il existe un n t e l L'orrourest o. ~ll=o.. e~-~_ que ~ u l t e es~ r6ordonn~e p o u r l o s t r a n s l a t i o n s sl ~ n'est pas constant: eZ" I~1~, a v e c " !
4 . 2 ) . cune permutation clrculaire, cholsissons cette derni~ro pour r~,d~ ~ . i , . ajor~ . ~ ~e ~ t ~f~rC~)].. ,O (<~,)] condition suffisante pour que cet ~eart tendevers O~quand ~ tend vers l'inflni est : ~~ (~ ~;')1 Compt~ tonu do ~o q,o s ~crlre ~'~ ~'C,d=o . ~o~o : Ainsi, la d6croissance de fine doit pas ~tre trop raplde. Pour que les permutations ~ solent r~ordonnantes pour la suite [~)L il suffit qu'~ 8 posltif donn6, les ense~les exceptionnels d'entiers E~ = $oient de fr~quencesasymptotique~nulles.