Phase portraits of linear type centers of polynomial hamiltonian systems with hamiltonian function of degree 5 of the form H = H1(x) + H2(y)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Martínez, Y. Paulina (Universidad del Bío-Bío. Departamento de Matemática)
Vidal, Claudio (Universidad del Bío-Bío. Departamento de Matemática)

Date:	2019
Abstract:	We study the phase portraits on the Poincaré disc for all the linear type centers of polynomial Hamiltonian systems of degree 5 with Hamiltonian function H(x, y) = H + H, where H = 1/2 x + a/3 x + a/4 x + a/5 x and H = 1/2 y + b/3 y + b/4 y + b/5 y as function of the six real parameters a, a, a, b, b and b with ab ≠ 0. We characterize the type and multiplicity of the roots of the polynomials p(y) = 1 + b + by + by and q(x) = 1 + ax + ax + ax and we prove that the finite equilibria are saddles, centers, cusps or the union of two hyperbolic sectors. For the infinite equilibria we found that there only exist two nodes on the Poincaré disc with opposite stability. We also characterize the separatrices of the equilibria and analyze the possible connections between them. As a complement we use the energy level to complete the global phase portrait.
Grants:	Ministerio de Economía y Competitividad MTM2016-77278-P Ministerio de Economía y Competitividad MTM2013-40998-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Separable Hamiltonian systems ; Linear type centers ; Phase portraits ; Quartic vector field
Published in:	Discrete and continuous dynamical systems. Series A, Vol. 39, Issue 1 (January 2019) , p. 75-113, ISSN 1553-5231

DOI: 10.3934/dcds.2019004

Postprint 35 p, 913.1 KB

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