Self-induced systems

被引：0
作者：
Fabien Durand
Nicholas Ormes
Samuel Petite
机构：
[1] Université de Picardie Jules Verne,Laboratoire Amiénois de Mathématiques Fondamentales et Appliquées, CNRS
[2] University of Denver,UMR 7352
来源：
Journal d'Analyse Mathématique | 2018年 / 135卷
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摘要：
A minimal Cantor system is said to be self-induced whenever it is conjugate to one of its induced systems. Substitution subshifts and some odometers are classical examples, and we show that these are the only examples in the equicontinuous or expansive case. Nevertheless, we exhibit a zero entropy self-induced system that is neither equicontinuous nor expansive. We also provide non-uniquely ergodic self-induced systems with infinite entropy. Moreover, we give a characterization of self-induced minimal Cantor systems in terms of substitutions on finite or infinite alphabets.
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页码：725 / 756
页数：31
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共 61 条
  • [1] Arnoux P.(1988)Un exemple de semi-conjugaison entre un échange d’intervalles et une translation sur le tore Bull. Soc. Math. France 116 489-500
  • [2] Arnoux P.(2001)Pisot substitutions and Rauzy fractals Bull Belg. Math. Soc. 8 181-207
  • [3] Ito S.(1991)Représentation géométrique de suites de complexité 2n + 1 Bull. Soc. Math. France 119 199-215
  • [4] Arnoux P.(1997)An extension of Lagrange’s theorem to interval exchange transformations over quadratic fields J. Anal. Math. 72 21-44
  • [5] Rauzy G.(2014)Topological conjugacy to given constant length substitution minimal systems Indag. Math. (N.S.) 25 646-651
  • [6] Boshernitzan M.(2009)Induced subsystems associated to a Cantor minimal system Colloq. Math. 117 207-221
  • [7] Carroll C. R.(2000)Orbit equivalence and Kakutani equivalence with Sturmian subshifts Studia Math. 142 25-45
  • [8] Coven E.(2009)Measured topological orbit and Kakutani equivalence Discrete Contin. Dyn Syst. Ser. S 2 221-238
  • [9] Dykstra A.(2008)Finite-rank Bratteli-Vershik diagrams are expansive Ergodic Theory Dynam. Systems 28 739-747
  • [10] Keane M.(1998)A characterization of substitutive sequences using return words Discrete Math. 179 89-101
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