Journal d'Analyse Mathématique

, Volume 135, Issue 2, pp 725–756 | Cite as

Self-induced systems

  • Fabien Durand
  • Nicholas Ormes
  • Samuel Petite


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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© Hebrew University Magnes Press 2018

Authors and Affiliations

  1. 1.Laboratoire Amiénois de Mathématiques Fondamentales et Appliquées, CNRS-UMR 7352Université de Picardie Jules VerneAmiens Cedex 1France
  2. 2.Department of MathematicsUniversity of DenverDenverUSA

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