On Dynamics Related to a Class of Numeration Systems |
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Authors: | Maria Doudékova-Puydebois |
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Affiliation: | (1) Université de Provence, Marseille, France, FR |
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Abstract: | In this paper, we investigate the class of numeration systems and we study the associated dynamical systems, called odometers. It is shown that these odometers are measure-theoretically isomorphic to rank one transformations on the unit interval, constructed by a cutting-stacking method. Furthermore, a symbolic coding leads to isomorphic shift systems arising from substitutions. Some skew products of the odometers by cocycles related to the sum of digits are shown to be ergodic. Received 5 March 2001; in revised form 16 August 2001 |
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Keywords: | 2000 Mathematics Subject Classification: 11A63 28D05 37A20 |
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