Finite-range topical functions and uniformly topical functions

Thierry Bousch (1) , Jean Mairesse (2)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay
2 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications

We introduce a remarkable subclass of the class of topical functions, the class of uniformly topical functions, whose dynamical behaviour is investigated. Every uniformly topical endo-function has a spectral vector, related to some special fixed points (possibly at infinity), about which we establish various properties. In the stochastic case, we prove a multiplicative ergodic theorem, asserting that the stochastic spectral vector exists in all cases.

Mots clés: Topical function; uniformly topical function; finite range; spectral vector; cycle time vector; multiplicative ergodic theorem.; multiplicative ergodic theorem

Domaines: Systèmes dynamiques [math.DS]

Thierry Bousch, Jean Mairesse. Finite-range topical functions and uniformly topical functions. Dynamical Systems An International Journal, 2006, 21 (1), pp.73-114. ⟨hal-00164818⟩