Isochronicity and normal forms of polynomial systems of ODEs

DOI10.1016/j.jsc.2011.12.039zbMath1248.34046OpenAlexW2058696474MaRDI QIDQ432742

Valery G. Romanovski, Mao'an Han

Publication date: 4 July 2012

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jsc.2011.12.039

zbMATH Keywords

normal formsisochronicitylinearizabilitypolynomial systems of ODE's

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Software, source code, etc. for problems pertaining to ordinary differential equations (34-04)

Related Items (10)

Rigid centres on the center manifold of tridimensional differential systems ⋮ Global phase portraits of uniform isochronous centers with quartic homogeneous polynomial nonlinearities ⋮ Center problem in the center manifold for quadratic differential systems in \(\mathbb{R}^3\) ⋮ Bounding the number of limit cycles for a polynomial Liénard system by using regular chains ⋮ Isochronicity and linearizability of a planar cubic system ⋮ A hybrid symbolic-numerical approach to the center-focus problem ⋮ An algorithm for providing the normal forms of spatial quasi-homogeneous polynomial differential systems ⋮ On the Topology of Isochronous Centers of Hamiltonian Differential Systems ⋮ Limit Cycles on Piecewise Smooth Vector Fields with Coupled Rigid Centers ⋮ Phase portraits of uniform isochronous quartic centers

Uses Software

• SINGULAR
• primdec

Cites Work

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• Localization and primary decomposition of polynomial ideals
• Strong isochronism of a center and a focus for systems with homogeneous nonlinearities
• Algorithmic derivation of isochronicity conditions
• Characterizing isochronous points and computing isochronous sections
• Gröbner bases and primary decomposition of polynomial ideals
• Elimination methods
• Local theory of nonlinear analytic ordinary differential equations
• Linearization of isochronous centers
• Isochronous and strongly isochronous oscillations of two-dimensional monodromic holomorphic dynamical systems
• Stability of motion
• Isochronous Centers in Planar Polynomial Systems
• The Center and Cyclicity Problems
• Bifurcation of Critical Periods for Plane Vector Fields
• P-adic reconstruction of rational numbers
• Linearizability of linear systems perturbed by fifth degree homogeneous polynomials
• Characterization of isochronous foci for planar analytic differential systems
• Nondegenerate linearizable centres of complex planar quadratic and symmetric cubic systems in \(\mathbb C^2\)

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