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Analytic integrability of Hamiltonian systems with exceptional potentials
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Valls, Clàudia 1973- (Universidade Técnica de Lisboa. Departamento de Matemática)

Date: 2015
Abstract: We study the existence of analytic first integrals of the complex Hamiltonian systems of the form H = 1 2 ∑ 2 i=1 p 2 i + Vl(q1, q2) with the homogeneous polynomial potential Vl(q1, q2) = α(q2 − iq1) L (q2 + iq1) k−l , l = 0, . . . , k, α ∈ C \ {0} of degree k called exceptional potentials. In Remark 2. 1 of J. Math. Phys. 46 (2005), 062901, the authors state: The exceptional potentials V0, V1, Vk−1, Vk and Vk/2 when k is even are integrable with a second polynomial first integral. However nothing is known about the integrability of the remaining exceptional potentials. Here we prove that the exceptional potentials with k even diferent from V0, V1, Vk−1, Vk and Vk/2, have no independent analytic first integral different from the Hamiltonian one. Additionally in the cases V2 and Vk−2 with k either even or odd we show that they do not have rational first integrals independent of the Hamiltonian.
Note: Agraïments: UNAB13-4E-1604. The second author is partially supported by FCT/Portugal through UID/MAT/04459/2013.
Note: Número d'acord de subvenció MINECO/MTM2008-03437
Note: Número d'acord de subvenció MINECO/MTM2013-40998-P
Note: Número d'acord de subvenció AGAUR/2014/SGR-568
Note: Número d'acord de subvenció EC/FP7/2012/316338
Note: Número d'acord de subvenció EC/FP7/2012/318999
Rights: Tots els drets reservats.
Language: Anglès
Document: article ; recerca ; acceptedVersion
Subject: Exceptional potential ; Hamiltonian system with 2 degrees of freedom ; Homogeneous potentials of degree k ; Integrability
Published in: Physics Letters. A, Vol. 379 (2015) , p. 2295-2299, ISSN 0375-9601

DOI: 10.1016/j.physleta.2015.07.034


Postprint
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The record appears in these collections:
Research literature > UAB research groups literature > Research Centres and Groups (scientific output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
Articles > Published articles

 Record created 2016-01-12, last modified 2020-08-16



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