The Cyclicity of a Cubic System

DOI10.1142/S1230161209000323zbMath1207.37039OpenAlexW2025022891MaRDI QIDQ5851894

Valery G. Romanovski, Alessandro Logar, Viktor Levandovskyy

Publication date: 26 January 2010

Published in: Open Systems & Information Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s1230161209000323

zbMATH Keywords

bifurcationlimit cyclecyclicityHilbert sixteenth problem

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)

Related Items (8)

On the multiple zeros of a real analytic function with applications to the averaging theory of differential equations ⋮ Center conditions and cyclicity for a family of cubic systems: computer algebra approach ⋮ Asymptotics and stability of the delayed Duffing equation ⋮ Cyclicity of nilpotent centers with minimum Andreev number ⋮ Estimating the number of limit cycles in polynomial systems ⋮ Cyclicity of polynomial nondegenerate centers on center manifolds ⋮ Cyclicity of a class of polynomial nilpotent center singularities ⋮ Bifurcation of critical periods of polynomial systems

Uses Software

• SINGULAR

Cites Work

• Localization and primary decomposition of polynomial ideals
• Quadratic systems with center and their perturbations
• Bernstein inequalities and applications to analytic geometry and differential equations
• The Sibirsky component of the center variety of polynomial differential systems.
• The cyclicity of a cubic system with nonradical Bautin ideal
• Bruno Buchberger's PhD thesis 1965: An algorithm for finding the basis elements of the residue class ring of a zero dimensional polynomial ideal. Translation from the German
• A new proof to Bautin's theorem
• On some open problems in planar differential systems and Hilbert's 16th problem
• Time-Reversibility in 2-Dimensional Systems
• The centre and isochronicity problems for some cubic systems
• HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
• Eleven small limit cycles in a cubic vector field

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