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Une propriété de domination convexe pour les orbites sturmiennes

  • Thierry Bousch (a1)
Abstract

Let x = (x0; x1; … ) be a N-periodic sequence of integers (N ≥ 1), and s a sturmian sequence with the same barycenter (and also N-periodic, consequently). It is shown that, for affine functions ∝: R N (N) → R which are increasing relatively to some order ≤2 on R N (N) (the space of all N-periodic sequences), the average of |∝| on the orbit of x is greater than its average on the orbit of s.

Résumé

Soit x = (x0; x1; … ) une suite N-périodique d'entiers (N ≥ 1), et s une suite sturmienne de même barycentre (et donc également N-périodique). On montre que, pour les fonctions affines ∝: R N (N) → R qui sont croissantes relativement à un certain ordre ≤2 sur R N (N) (l'espace de toutes les suites N-périodiques), la moyenne de |∝| sur l'orbite de x est plus grande que sa moyenne sur l'orbite de s.

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Canadian Journal of Mathematics
  • ISSN: 0008-414X
  • EISSN: 1496-4279
  • URL: /core/journals/canadian-journal-of-mathematics
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