Simultaneous bifurcation of limit cycles from a linear center with extra singular points

DOI10.1016/j.bulsci.2013.09.004zbMath1295.34046OpenAlexW2076673476MaRDI QIDQ2637615

Joan Torregrosa, Set Pérez-González

Publication date: 13 February 2014

Published in: Bulletin des Sciences Mathématiques (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.bulsci.2013.09.004

zbMATH Keywords

piecewise rational Abelian integralpolynomial perturbation of centerssimultaneous limit cycles bifurcations

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) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08)

Related Items (3)

Simultaneity of centres in ℤ _q -equivariant systems ⋮ Simultaneous bifurcation of limit cycles from a cubic piecewise center with two period annuli ⋮ Simultaneity of centres in double-reversible planar differential systems

Cites Work

• Unnamed Item
• Unnamed Item
• Upper bounds for the number of zeroes for some abelian integrals
• Global bifurcation of limit cycles in a family of polynomial systems
• Limit cycles of cubic polynomial vector fields via the averaging theory
• Bifurcation of limit cycles from a polynomial non-global center
• Quadratic perturbations of a class of quadratic reversible systems with two centers
• Linear estimation of the number of zeros of abelian integral for some cubic isochronous centers
• Interpolation and approximation by polynomials
• Perturbation from an elliptic Hamiltonian of degree four. IV: Figure eight-loop.
• Limit cycles of a perturbed cubic polynomial differential center
• Simultaneous bifurcation of limit cycles from two nests of periodic orbits
• Linear estimate for the number of zeros of Abelian integrals for quadratic isochronous centres
• HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
• GLOBAL BIFURCATION OF LIMIT CYCLES IN A FAMILY OF MULTIPARAMETER SYSTEM
• Polynomial systems: a lower bound for the Hilbert numbers

This page was built for publication: Simultaneous bifurcation of limit cycles from a linear center with extra singular points