An algorithm for providing the normal forms of spatial quasi-homogeneous polynomial differential systems

DOI10.1016/j.jsc.2018.08.006zbMath1428.34049OpenAlexW2890005946MaRDI QIDQ2000259

Antón Lombardero, Belén García, Jesús S. Pérez del Río, Jaume Llibre

Publication date: 28 June 2019

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

Full work available at URL: https://ddd.uab.cat/record/221303

zbMATH Keywords

algorithmweight vectorquasi-homogeneouspolynomial differential system

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Differential algebra (12H05) Abstract differential equations (12H20) Computational methods for problems pertaining to field theory (12-08)

Related Items (1)

Analytic integrability of quasi-homogeneous systems via the Yoshida method

Uses Software

• counterQH.m

Cites Work

• Isochronicity and normal forms of polynomial systems of ODEs
• Center of planar quintic quasi-homogeneous polynomial differential systems
• Kovalevskaya exponents and the space of initial conditions of a quasi-homogeneous vector field
• Global behaviour of the period function of the sum of two quasi-homogeneous vector fields
• Classification of global phase portraits of planar quartic quasi-homogeneous polynomial differential systems
• Classification and counting of planar quasi-homogeneous differential systems through their weight vectors
• Rational integrals of quasi-homogeneous dynamical systems
• Planar quasi-homogeneous polynomial differential systems and their integrability
• The limit set of trajectory in quasi-homogeneous system in ℝ³
• Centers of projective vector fields of spatial quasi-homogeneous systems with weight <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo form="prefix">(</mml:mo> <mml:mi>m</mml:mi> <mml:mo>,</mml:mo> <mml:mi>m</mml:mi> <mml:mo>,</mml:mo> <mml:mi>n</mml:mi> <mml:mo form="postfix">)</mml:mo> </mml:mrow> </mml:math> and degree <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> on the sphere
• Polynomial first integrals for quasi-homogeneous polynomial differential systems
• On the Limit Cycles Bifurcating from Piecewise Quasi-Homogeneous Differential Center
• Center Problems and Limit Cycle Bifurcations in a Class of Quasi-Homogeneous Systems
• Bifurcation of Limit Cycles from a Quasi-Homogeneous Degenerate Center
• Necessary condition for the existence of algebraic first integrals

This page was built for publication: An algorithm for providing the normal forms of spatial quasi-homogeneous polynomial differential systems