Bifurcation diagrams and global phase portraits for some hamiltonian systems with rational potentials

In this paper, we study the global dynamical behavior of the Hamiltonian system ẋ = Hy(x,y), ẏ=-Hx(x,y) with the rational potential Hamiltonian H(x,y) = y2/2 + P(x)/Q(y), where P(x) and Q(y) are polynomials of degree 1 or 2. First we get the normal forms for these rational Hamiltonian systems by som...

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Detalles Bibliográficos
Autores: Chen, Ting|||0000-0001-6570-885X, Llibre, Jaume|||0000-0002-9511-5999
Tipo de recurso: artículo
Fecha de publicación:2018
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:221301
Acceso en línea:https://ddd.uab.cat/record/221301
https://dx.doi.org/urn:doi:10.1142/S0218127418501687
Access Level:acceso abierto
Palabra clave:Rational Hamiltonian system
Equilibrium point
Infinity
Phase portrait
Bifurcation diagram
Descripción
Sumario:In this paper, we study the global dynamical behavior of the Hamiltonian system ẋ = Hy(x,y), ẏ=-Hx(x,y) with the rational potential Hamiltonian H(x,y) = y2/2 + P(x)/Q(y), where P(x) and Q(y) are polynomials of degree 1 or 2. First we get the normal forms for these rational Hamiltonian systems by some linear change of variables. Then we classify all the global phase portraits of these systems in the Poincaré disk and provide their bifurcation diagrams.