Bifurcation diagrams and global phase portraits for some hamiltonian systems with rational potentials
Chen, Ting (Hunan University. College of Mathematics and Econometrics.)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2018
Abstract:	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.
Grants:	Ministerio de Economía y Competitividad MTM2016-77278-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 European Commission 777911
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Rational Hamiltonian system ; Equilibrium point ; Infinity ; Phase portrait ; Bifurcation diagram
Published in:	International journal of bifurcation and chaos in applied sciences and engineering, Vol. 28, Issue 13 (December 2018) , art. 1850168, ISSN 1793-6551

DOI: 10.1142/S0218127418501687

Postprint 43 p, 856.0 KB

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