Cyclicity versus center problem

DOI10.1007/s12346-010-0022-9zbMath1210.34049OpenAlexW2038985136MaRDI QIDQ611136

Jaume Giné, Armengol Gasull

Publication date: 14 December 2010

Published in: Qualitative Theory of Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12346-010-0022-9

zbMATH Keywords

limit cyclesLyapunov constantscyclicitypolynomial differential systemfocal quantities

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) 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) Periodic orbits of vector fields and flows (37C27)

Related Items (13)

Persistent centers of complex systems ⋮ Cyclicity of a simple focus via the vanishing multiplicity of inverse integrating factors ⋮ Bifurcation of 2-periodic orbits from non-hyperbolic fixed points ⋮ Local bifurcation of limit cycles and integrability of a class of nilpotent systems ⋮ Weak-foci of high order and cyclicity ⋮ Center conditions and bifurcation of limit cycles at three-order nilpotent critical point in a cubic Lyapunov system ⋮ Local bifurcation of limit cycles and center problem for a class of quintic nilpotent systems ⋮ Center conditions and bifurcation of limit cycles at three-order nilpotent critical point in a septic Lyapunov system ⋮ Center conditions and cyclicity for a family of cubic systems: computer algebra approach ⋮ BIFURCATION OF LIMIT CYCLES AT A NILPOTENT CRITICAL POINT IN A SEPTIC LYAPUNOV SYSTEM ⋮ Absolute cyclicity, Lyapunov quantities and center conditions ⋮ On the multiplicity of algebraic limit cycles ⋮ Essential perturbations of polynomial vector fields with a period annulus

Cites Work

• Unnamed Item
• Higher order bifurcations of limit cycles
• On the integrability of two-dimensional flows
• Quadratic systems with center and their perturbations
• Bifurcation of planar vector fields and Hilbert's sixteenth problem
• A relation between small amplitude and big limit cycles.
• Hopf-Takens bifurcations and centres
• Absolute cyclicity, Lyapunov quantities and center conditions
• A new approach to the computation of the Lyapunov constants
• Configurations of zeroes of analytic functions
• Algebraic curves of maximal cyclicity
• Centennial History of Hilbert's 16th Problem
• On the Poincaré–Lyapunov constants and the Poincare series
• HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
• Successive derivatives of a first return map, application to the study of quadratic vector fields
• Algorithmic Derivation of Centre Conditions
• Melnikov functions and Bautin ideal

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