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Pàgina inicial > Articles > Articles publicats > Phase portraits of linear type centers of polynomial hamiltonian systems with hamiltonian function of degree 5 of the form H = H1(x) + H2(y) |
Data: | 2019 |
Resum: | 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. |
Ajuts: | 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 |
Drets: | Tots els drets reservats. |
Llengua: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Matèria: | Separable Hamiltonian systems ; Linear type centers ; Phase portraits ; Quartic vector field |
Publicat a: | Discrete and continuous dynamical systems. Series A, Vol. 39, Issue 1 (January 2019) , p. 75-113, ISSN 1553-5231 |
Postprint 35 p, 913.1 KB |