Polynomial entropies for Bott nondegenerate Hamiltonian systems
Polynomial entropies for Bott nondegenerate Hamiltonian systems
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. We prove that, under conditions on the critical level of the Bott first integral and dynamical conditions on the hamiltonian function, the weak polynomial entropy belongs to {0,1} and the polynomial entropy belongs to {0,1,2}.
45 pages
- French National Centre for Scientific Research France
- Sorbonne Paris Cité France
- University of Paris France
- Institut de Mathématiques de Jussieu France
- Université Paris Descartes France
FOS: Mathematics, [MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS], Dynamical Systems (math.DS), Mathematics - Dynamical Systems, [MATH.MATH-DG] Mathematics [math]/Differential Geometry [math.DG]
FOS: Mathematics, [MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS], Dynamical Systems (math.DS), Mathematics - Dynamical Systems, [MATH.MATH-DG] Mathematics [math]/Differential Geometry [math.DG]
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