POLYNOMIAL ENTROPIES FOR BOTT NONDEGENERATE HAMILTONIAN SYSTEMS
Résumé
In this paper, we study the entropy of a Hamiltonian flow in restriction to an enregy level where it admits a first integral which is nondegenerate in the Bott sense. It is easy to see that for such a flow, the topological entropy vanishes. We focus on the polynomial and the weak polynomial entropies h pol and h pol *. We prove that, under conditions on the critical level of the Bott first integral and dynamical conditions on the hamiltonian function H, h * pol ∈ {0, 1} and h pol ∈ {0, 1, 2}.
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