Perturbation from an asymmetric cubic Hamiltonian

DOI10.1016/j.jmaa.2004.12.044zbMath1077.34038OpenAlexW1977878867MaRDI QIDQ1773316

Hong Zang, Tonghua Zhang, Mao'an Han

Publication date: 28 April 2005

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2004.12.044

zbMATH Keywords

stabilitybifurcationlimit cycleHamiltonian systemHilbert's 16th problem

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07)

Related Items (8)

The number and distributions of limit cycles for a class of cubic near-Hamiltonian systems ⋮ Limit cycles for the kukles system ⋮ On the zeros of the Abelian integrals for a class of Liénard systems ⋮ Bifurcations and distribution of limit cycles for near-Hamiltonian polynomial systems ⋮ Linear estimate of the number of limit cycles for a class of nonlinear systems ⋮ Bifurcations of limit cycles from quintic Hamiltonian systems with a double figure eight loop ⋮ EXISTENCE CONDITIONS OF THIRTEEN LIMIT CYCLES IN A CUBIC SYSTEM ⋮ Thirteen limit cycles for a class of cubic Hamiltonian system with higher-order perturbed terms

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Bifurcations of limit cycles forming compound eyes in the cubic system
• Dynamics retrospective: Great problems, attempts that failed
• Some properties of planar polynomial systems of even degree
• The distribution of limit cycles in quadratic systems with four finite singularities
• Higher order bifurcations of limit cycles
• Bifurcation of planar vector fields and Hilbert's sixteenth problem
• Cyclicity of planar homoclinic loops and quadratic integrable systems
• Finite cyclicity of graphics with a nilpotent singularity of saddle or elliptic type
• On the number of limit cycles in double homoclinic bifurcations
• Bifurcations of limit cycles for a cubic Hamiltonian system under quartic perturbations
• Perturbation from a cubic Hamiltonian with three figure eight-loops
• Bifurcation from a periodic orbit in perturbed planar Hamiltonian systems.
• Perturbation from an elliptic Hamiltonian of degree four. IV: Figure eight-loop.
• On the stability of double homoclinic and heteroclinic cycles.
• Computation of the center isochronism conditions for polynomial systems
• Bifurcations of limit cycles in a cubic system
• A cubic Kolmogorov system with six limit cycles
• A numerical approach to bifurcations from quadratic centers
• A new approach to the computation of the Lyapunov constants
• A family of quadratic polynomial differential systems with invariant algebraic curves of arbitrarily high degree without rational first integrals
• New Directions in Dynamical Systems
• On the global analysis of the planar quadratic vector fields
• HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
• INVESTIGATIONS OF BIFURCATIONS OF LIMIT CYCLES IN Z₂-EQUIVARIANT PLANAR VECTOR FIELDS OF DEGREE 5
• Bifurcations of Limit Cycles From Infinity in Quadratic Systems
• The Geometry of Quadratic Differential Systems with a Weak Focus of Third Order
• Eleven small limit cycles in a cubic vector field
• ON THE NUMBER AND DISTRIBUTION OF LIMIT CYCLES IN A CUBIC SYSTEM
• Bifurcations of limit cycles from quintic Hamiltonian systems with a double figure eight loop

This page was built for publication: Perturbation from an asymmetric cubic Hamiltonian