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Article Dans Une Revue Proceedings of the London Mathematical Society Année : 2005

Patterns and minimal dynamics for graph maps

Résumé

We study the rigidity problem for periodic orbits of (continuous) graph maps belonging to the same homotopy equivalence class. Since the underlying spaces are not necessarily homeomorphic, we define a new notion of pattern which enables us to compare periodic orbits of self-maps of homotopyequivalent spaces. This definition unifies the known notions of pattern for other spaces. The two main results of the paper are: given a free group endomorphism, we study the persistence under homotopy of the periodic orbits of its topological representatives, and in the irreducible case, we prove the minimality (within the homotopy class) of the set of periodic orbits of its efficient representatives.
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Dates et versions

hal-00808807 , version 1 (07-04-2013)

Identifiants

  • HAL Id : hal-00808807 , version 1

Citer

Lluis Alsédà, François Gautero, John Guaschi, Jérôme Los, Francesc Mañosas, et al.. Patterns and minimal dynamics for graph maps. Proceedings of the London Mathematical Society, 2005, 91 (3), pp.414-442. ⟨hal-00808807⟩
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