Perturbation from an asymmetric cubic Hamiltonian
type: Item
instance of: scholarly article
title: Perturbation from an asymmetric cubic Hamiltonian
zbMATH Open document ID: 1077.34038
author: Tonghua Zhang
author: Hong Zang
author: Maoan Han
published in: Journal of Mathematical Analysis and Applications
publication date: 2005-04-28T00:00:00Z
review text: The paper is devoted to possible distributions and a number of limit cycles appearing from an asymmetric Hamiltonian system of degree three under cubic perturbations. The most interesting result is that such system can have 11 limit cycles with three different distributions, two of them are new.
reviewed by: Alexander Grin
Mathematics Subject Classification ID: 34C07
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C05
zbMATH DE Number: 2162026
zbMATH Keywords: Hamiltonian system
zbMATH Keywords: bifurcation
zbMATH Keywords: Hilbert's 16th problem
zbMATH Keywords: limit cycle
zbMATH Keywords: stability
MaRDI profile type: Publication
full work available at URL: j.jmaa.2004.12.044
OpenAlex ID: W1977878867
cites work: Q5832271
cites work: New Directions in Dynamical Systems
cites work: Q3785183
cites work: A family of quadratic polynomial differential systems with invariant algebraic curves of arbitrarily high degree without rational first integrals
cites work: Perturbation from an elliptic Hamiltonian of degree four. IV: Figure eight-loop.
cites work: Some properties of planar polynomial systems of even degree
cites work: A new approach to the computation of the Lyapunov constants
cites work: Bifurcations of Limit Cycles From Infinity in Quadratic Systems
cites work: Cyclicity of planar homoclinic loops and quadratic integrable systems
cites work: On the number of limit cycles in double homoclinic bifurcations
cites work: On the stability of double homoclinic and heteroclinic cycles.
cites work: ON THE NUMBER AND DISTRIBUTION OF LIMIT CYCLES IN A CUBIC SYSTEM
cites work: Bifurcation from a periodic orbit in perturbed planar Hamiltonian systems.
cites work: Higher order bifurcations of limit cycles
cites work: HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
cites work: Bifurcations of limit cycles forming compound eyes in the cubic system
cites work: INVESTIGATIONS OF BIFURCATIONS OF LIMIT CYCLES IN Z2-EQUIVARIANT PLANAR VECTOR FIELDS OF DEGREE 5
cites work: Q4674227
cites work: The Geometry of Quadratic Differential Systems with a Weak Focus of Third Order
cites work: A cubic Kolmogorov system with six limit cycles
cites work: Computation of the center isochronism conditions for polynomial systems
cites work: Bifurcation of planar vector fields and Hilbert's sixteenth problem
cites work: Finite cyclicity of graphics with a nilpotent singularity of saddle or elliptic type
cites work: On the global analysis of the planar quadratic vector fields
cites work: A numerical approach to bifurcations from quadratic centers
cites work: Dynamics retrospective: Great problems, attempts that failed
cites work: Q3715459
cites work: Q4002482
cites work: The distribution of limit cycles in quadratic systems with four finite singularities
cites work: Bifurcations of limit cycles in a cubic system
cites work: Bifurcations of limit cycles from quintic Hamiltonian systems with a double figure eight loop
cites work: Perturbation from a cubic Hamiltonian with three figure eight-loops
cites work: Bifurcations of limit cycles for a cubic Hamiltonian system under quartic perturbations
cites work: Eleven small limit cycles in a cubic vector field
DOI: 10.1016/J.JMAA.2004.12.044
description: scientific article; zbMATH DE number 2162026