On the period function of centers in planar polynomial Hamiltonian systems of degree four.

DOI10.1007/BF02969337zbMath1055.34057MaRDI QIDQ1415972

Xavier Jarque, Jordi Villadelprat

Publication date: 9 December 2003

Published in: Qualitative Theory of Dynamical Systems (Search for Journal in Brave)

zbMATH Keywords

isochronicityperiod functionHamiltonian systems of degree 4

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99)

Cites Work

• Unnamed Item
• Geometric methods for two-point nonlinear boundary value problems
• Darboux linearization and isochronous centers with a rational first integral
• The monotonicity of the period function for planar Hamiltonian vector fields
• Global bifurcation of steady-state solutions
• The period function for Hamiltonian systems with homogeneous nonlinearities
• Period function for a class of Hamiltonian systems
• Nonexistence of isochronous centers in planar polynomial Hamiltonian systems of degree four
• Isochronicity for several classes of Hamiltonian systems
• Linearization of isochronous centers
• Isochronous Centers in Planar Polynomial Systems
• A class of Hamiltonian systems with increasing periods.
• Bifurcation of Critical Periods for Plane Vector Fields
• Local Bifurcations of Critical Periods in the Reduced Kukles System

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