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This article is cited in 17 scientific papers (total in 17 papers)
Polynomial Entropies for Bott Integrable Hamiltonian Systems
Clémence Labrousseab, Jean-Pierre Marcoc a Université Paris-Dauphine, CEREMADE,
Place du Maréchal de Lattre de Tassigny 75775 Paris cedex 16, France
b École Normale Supérieure, DMA,
45 rue d’Ulm F-75230 Paris Cedex 05, France
c Université Paris 6, Analyse Algébrique, 4 Place Jussieu, 75252 Paris cedex 05, France
Abstract:
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 ${\rm{h_{pol}}}$ and ${\rm{h_{pol}^*}}$. We show that, under
natural conditions on the critical levels of the Bott first integral and
on the Hamiltonian function $H$, ${\rm{h_{pol}^*}}\in \{0,1\}$ and ${\rm{h_{pol}}}\in \{0,1,2\}$.
To prove this result, our main tool is a semi-global desingularization of
the Hamiltonian system in the neighborhood of a polycycle.
Keywords:
dynamical complexity, entropy, integrability, Bott integrable Hamiltonians.
Received: 13.01.2014 Accepted: 27.04.2014
Citation:
Clémence Labrousse, Jean-Pierre Marco, “Polynomial Entropies for Bott Integrable Hamiltonian Systems”, Regul. Chaotic Dyn., 19:3 (2014), 374–414
Linking options:
https://www.mathnet.ru/eng/rcd161 https://www.mathnet.ru/eng/rcd/v19/i3/p374
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Abstract page: | 163 | References: | 35 |
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