Finite-range topical functions and uniformly topical functions |
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| Authors: | Thierry Bousch Jean Mairesse |
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| Affiliation: | 1. Laboratoire de Mathématique (UMR 8628 du CNRS), bat. 425/430 , Université de Paris-Sud , 91405 Orsay Cedex, France;2. LIAFA , CNRS et Université Paris 7 , case 7014, 2 place Jussieu, 75251 Paris Cedex 05, France |
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| Abstract: | 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 endofunction 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. |
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