CRITICAL PERIODS OF THIRD-ORDER PLANAR HAMILTONIAN SYSTEMS

DOI10.1142/S0218127410027040zbMath1196.34049MaRDI QIDQ4933409

Jizhou Zhang, Pei Yu, Mao'an Han

Publication date: 12 October 2010

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

zbMATH Keywords

centernormal formHamiltonian systemcritical periods

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Bifurcation problems for finite-dimensional Hamiltonian and Lagrangian systems (37J20) Bifurcation theory for ordinary differential equations (34C23)

Related Items

Small amplitude limit cycles and local bifurcation of critical periods for a quartic Kolmogorov system, Bi-center conditions and local bifurcation of critical periods in a switching \(Z_2\) equivariant cubic system, Isolated periodic wave trains and local critical wave lengths for a nonlinear reaction-diffusion equation, Bifurcations of Critical Periods for a Class of Quintic Liénard Equation, Criticality via first order development of the period constants, New lower bounds of the number of critical periods in reversible centers, Weak Bi-Center and Critical Period Bifurcations of a Z2-Equivariant Quintic System, LOCAL BIFURCATION OF CRITICAL PERIODS IN QUADRATIC-LIKE CUBIC SYSTEMS, Unnamed Item, Bifurcation of critical periods of polynomial systems

Cites Work

• Unnamed Item
• Weak centers and bifurcation of critical periods in reversible cubic systems
• Twelve limit cycles in a cubic order planar system with \(Z_2\) symmetry
• COMPUTATION OF NORMAL FORMS VIA A PERTURBATION TECHNIQUE
• Some cubic systems with several limit cycles
• CRITICAL PERIODS OF PLANAR REVERTIBLE VECTOR FIELD WITH THIRD-DEGREE POLYNOMIAL FUNCTIONS
• A NOTE ON THE CRITICAL PERIODS OF POTENTIAL SYSTEMS
• Local Bifurcation of Critical Periods in Vector Fields With Homogeneous Nonlinearities of the Third Degree
• HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
• Polynomial systems: a lower bound for the Hilbert numbers
• TWELVE LIMIT CYCLES IN A CUBIC CASE OF THE 16th HILBERT PROBLEM