Types d'orbites et dynamique minimale pour les applications continues de graphesOrbit types and minimal dynamics for graph maps |
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| Authors: | Ll Alsedà F Gautero J Guaschi J Los F Mañosas P Mumbrú |
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| Institution: | 1. Universitat Autònoma de Barcelona, Departament de Matemàtiques, Edifici Cc, 08913 Cerdanyola del Vallès, Barcelona, Espagne;2. Laboratoire AGAT, Université Lille I, Bât. M2, 59655 Villeneuve d''Ascq, France;3. Laboratoire de mathématiques E. Picard, Université Toulouse III, 118, route de Narbonne, 31062 Toulouse cedex 4, France;4. Centre de mathématiques et informatique, Université Aix-Marseille I, 39, rue F. Joliot Curie, 13453 Marseille cedex 13, France;5. Universitat de Barcelona, Departament de Matemàtica Aplicada i Anàlisi, Gran Via 585, 08071 Barcelona, Espagne |
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| Abstract: | We define the type of a periodic orbit of a graph map. We consider the class of ‘train-track’ representatives, that is, those graph maps which minimise the topological entropy of the topological representatives of a given free group endomorphism. We prove that each type of periodic orbit realised by an efficient representative is also realised by any representative of the same free group endomorphism. Moreover, the number of periodic orbits of a given type is minimised by the efficient representatives. To cite this article: Ll. Alsedà et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 479–482. |
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