Center problem in the center manifold for quadratic and cubic differential systems in \(\mathbb{R}^3\)

DOI10.1016/j.amc.2014.11.057zbMath1328.34029OpenAlexW2013532653MaRDI QIDQ902990

Claudia Valls

Publication date: 4 January 2016

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2014.11.057

zbMATH Keywords

first integralscenter manifoldscenter-focus problem

Mathematics Subject Classification ID

Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07)

Related Items

The generalized polynomial Moon-Rand system, Center problem in the center manifold for quadratic differential systems in \(\mathbb{R}^3\), A hybrid symbolic-numerical approach to the center-focus problem, Study on dynamic behaviors of rotor model with coupling faults and applications of TPOD method

Uses Software

• SINGULAR
• primdec

Cites Work

• The center problem on a center manifold in \(\mathbb{R}^{3}\)
• Existence of inverse Jacobi multipliers around Hopf points in \(\mathbb R^3\): emphasis on the center problem
• Classification of the centers and their isochronicity for a class of polynomial differential systems of arbitrary degree
• Gröbner bases and primary decomposition of polynomial ideals
• Applications of centre manifold theory
• Stability and periodic oscillations in the Moon-Rand systems
• On some open problems in planar differential systems and Hilbert's 16th problem
• The nondegenerate center problem and the inverse integrating factor
• CENTER PROBLEM FOR THIRD-ORDER ODEs
• The Center and Cyclicity Problems