Uniqueness of limit cycles and quotients of abelian integrals

DOI10.1016/S0362-546X(96)00361-6zbMath0894.34023MaRDI QIDQ4378720

Josef Hainzl

Publication date: 7 September 1998

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

zbMATH Keywords

uniquenesslimit cyclesperturbed systemclosed orbitsquadratic systemsAbelian integralsperturbed Lotka-Volterra system

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05)

Related Items (1)

Linear estimate on the number of zeros of Abelian integrals for quadratic centers having almost all their orbits formed by cubics

Cites Work

• Zeros of special abelian integrals in a real domain
• Abelian integrals and bifurcation theory
• Bifurcations of planar vector fields. Nilpotent singularities and Abelian integrals
• Quadratic systems with center and their perturbations
• On saddle-loop bifurcations of limit cycles in perturbations of quadratic Hamiltonian systems
• Bifurcation of limit cycles in a particular class of quadratic systems with two centres
• On the number of limit cycles in perturbations of a two dimensional nonlinear differential system
• Limit cycles of perturbations of quadratic Hamiltonian vector fields
• A criterion for determining the monotonicity of the ratio of two Abelian integrals
• ON THE VERSALITY OF A FAMILY OF SYMMETRIC VECTOR FIELDS IN THE PLANE
• Multiparameter Bifurcation of a Predator-Prey System
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