Global Orbit Patterns for One Dimensional Dynamical Systems

René Lozi (1) , Clarisse Fiol (1)

1 JAD - Laboratoire Jean Alexandre Dieudonné

We study the behaviour of discrete one-dimensional dynamical systems associated to functions on finite sets. We formalise the global orbit pattern formed by all the periodic orbits (gop) as the ordered set of periods when the initial value thumbs the finite set in the increasing order. We are able to predict, using closed formulas, the number of gop for the set of all the functions on X. We also explore by computer experiments special subsets of this set of functions in which interesting patterns of gop are found.

Mots clés: dynamical systems; chaotic analysis; combinatorial dynamics; global orbit pattern; locally bounded range set

Domaines: Systèmes dynamiques [math.DS]

René Lozi, Clarisse Fiol. Global Orbit Patterns for One Dimensional Dynamical Systems. Grazer Math. Ber., 2009, ITERATION THEORY (ECIT ‘08), A.N. Sharkovsky, I.M. Sushko (Eds.) (354), pp.112-144. ⟨hal-00361853v3⟩