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Polynomial entropies for Bott integrable Hamiltonian systems

Labrousse, Clémence; Marco, Jean-Pierre (2014), Polynomial entropies for Bott integrable Hamiltonian systems, Regular and Chaotic Dynamics, 19, 3, p. 374-414. http://dx.doi.org/10.1134/S1560354714030083

Type
Article accepté pour publication ou publié
External document link
http://arxiv.org/abs/1207.4937v1
Date
2014
Journal name
Regular and Chaotic Dynamics
Volume
19
Number
3
Publisher
Springer
Pages
374-414
Publication identifier
Metadata
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Author(s)
Labrousse, Clémence
Marco, Jean-Pierre
Abstract (EN)
In this paper, we study the entropy of a Hamiltonian flow in restriction to an energy level where it admits a first integral which is nondegenerate in the sense of Bott. It is easy to see that for such a flow, the topological entropy vanishes. We focus on the polynomial and the weak polynomial entropies hpol and h pol * . We show that, under natural conditions on the critical levels of the Bott first integral and on the Hamiltonian function H, h pol * ∈ {0, 1} and hpol ∈ {0, 1, 2}. To prove this result, our main tool is a semi-global desingularization of the Hamiltonian system in the neighborhood of a polycycle.
Subjects / Keywords
dynamical complexity; entropy; integrability; Bott integrable Hamiltonians