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 publiéExternal document link
http://arxiv.org/abs/1207.4937v1Date
2014Journal name
Regular and Chaotic DynamicsVolume
19Number
3Publisher
Springer
Pages
374-414
Publication identifier
Metadata
Show full item recordAbstract (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 HamiltoniansRelated items
Showing items related by title and author.
-
Bounemoura, Abed; Kaloshin, Vadim (2016) Article accepté pour publication ou publié
-
Ben Abdallah, Naoufel; Dolbeault, Jean (2000) Article accepté pour publication ou publié
-
Set-valued solutions to the Cauchy problem for hyperbolic systems of partial differential inclusions Aubin, Jean-Pierre; Frankowska, Halina (1997) Article accepté pour publication ou publié
-
Aubin, Jean-Pierre; Day, Richard H. (1980) Article accepté pour publication ou publié
-
Perlat, Jean-Pierre; Le Tallec, Patrick (2000) Article accepté pour publication ou publié