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

Ting Chen, Jaume Llibre

Research output: Contribution to journalArticleResearch

2 Citations (Scopus)

Abstract

© World Scientific Publishing Company. In this paper, we study the global dynamical behavior of the Hamiltonian system á = Hy(x,y), á? = a '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.
Original languageEnglish
Article number1850168
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume28
DOIs
Publication statusPublished - 15 Dec 2018

Keywords

  • Bifurcation diagram
  • Equilibrium point
  • Infinity
  • Phase portrait
  • Rational Hamiltonian system

Fingerprint Dive into the research topics of 'Bifurcation diagrams and global phase portraits for some hamiltonian systems with rational potentials'. Together they form a unique fingerprint.

Cite this