Periodic solutions for the generalized anisotropic Lennard-Jones Hamiltonian
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Long, Yiming (Nankai University(China). Chern Institute of Mathematics and LPMC)

Date:	2015
Abstract:	We characterize the circular periodic solutions of the generalized Lennard-Jones Hamiltonian system with two particles in Rn, and we analyze what of these periodic solutions can be continued to periodic solutions of the anisotropic generalized Lennard-Jones Hamiltonian system. We also characterize the periods of antiperiodic solutions of the generalized Lennard-Jones Hamiltonian system on R2n, and prove the existences of 0 < τ∗ ≤ τ∗∗ such that this system possesses no τ /2-antiperiodic solution for all τ ∈ (0, τ∗), at least one τ /2-antiperiodic solution when τ = τ∗, precisely 2n families of τ /2-antiperiodic circular solutions when τ = τ∗∗, and precisely 2n+1 families of τ /2-antiperiodic circular solutions when τ > τ∗∗. Each of these circular solution families is of dimension n − 1 module the S1-action.
Grants:	Ministerio de Economía y Competitividad MTM2008-03437 Ministerio de Economía y Competitividad MTM2013-40998-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 European Commission 318999 European Commission 316338
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Anisotropic Lennard-Jones potential ; Circular periodic solutions ; Lennard-Jones potential
Published in:	Qualitative theory of dynamical systems, Vol. 14 (2015) , p. 291-311, ISSN 1662-3592

DOI: 10.1007/s12346-015-0167-7

Postprint 16 p, 425.7 KB

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