Infinite periodic points of endomorphisms over special confluent rewriting systems
Annales de l'Institut Fourier, Volume 59 (2009) no. 2, pp. 769-810.

We consider endomorphisms of a monoid defined by a special confluent rewriting system that admit a continuous extension to the completion given by reduced infinite words, and study from a dynamical viewpoint the nature of their infinite periodic points. For prefix-convergent endomorphisms and expanding endomorphisms, we determine the structure of the set of all infinite periodic points in terms of adherence values, bound the periods and show that all regular periodic points are attractors.

On considère les endomorphismes d’un monoïde défini par un système de réécriture spécial confluent qui admettent une extension continue à sa complétion donnée par les mots infinis réduits, et on étudie d’un point de vue dynamique la nature de leurs points périodiques infinis. Pour les endomorphismes préfixe-convergents et les endomorphismes expansifs, on détermine la structure de l’ensemble de tous les points périodiques infinis en termes de valeurs d’adhérence, on borne les périodes et on prouve que tous les points périodiques réguliers sont des attracteurs.

Received:
Accepted:
DOI: 10.5802/aif.2447
Classification: 68R15,  37B10,  20M35,  68Q70
Keywords: Periodic points, endomorphisms, rewriting systems, dynamics
Cassaigne, Julien 1; Silva, Pedro V. 2

1 Institut de Mathématiques de Luminy Case 907 13288 Marseille Cedex 9 (France)
2 Universidade do Porto Centro de Matemática Faculdade de Ciências R. Campo Alegre 687 4169-007 Porto (Portugal)
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Cassaigne, Julien; Silva, Pedro V. Infinite periodic points  of endomorphisms over special confluent rewriting systems. Annales de l'Institut Fourier, Volume 59 (2009) no. 2, pp. 769-810. doi : 10.5802/aif.2447. https://aif.centre-mersenne.org/articles/10.5802/aif.2447/

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