The center problem for \(\mathbb{Z}_2\)-symmetric nilpotent vector fields

DOI10.1016/j.jmaa.2018.05.079zbMath1395.34047OpenAlexW2807198515MaRDI QIDQ1645117

Jaume Giné, Jaume Llibre, Cristóbal García, Antonio Algaba

Publication date: 28 June 2018

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2018.05.079

zbMATH Keywords

center problemnilpotent center\(\mathbb{Z}_2\)-symmetric differential systems

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)

Related Items (13)

Algebraic integrability of nilpotent planar vector fields ⋮ Monodromic nilpotent singular points with odd Andreev number and the center problem ⋮ New criterions on stability and order of analytic nilpotent foci ⋮ Center conditions to find certain degenerate centers with characteristic directions ⋮ Complex integrability and linearizability of cubic \(Z_2\)-equivariant systems with two \(1:q\) resonant singular points ⋮ Center problem for generic degenerate vector fields ⋮ Center cyclicity for some nilpotent singularities including the ℤ2-equivariant class ⋮ Cyclicity of nilpotent centers with minimum Andreev number ⋮ Center conditions of a particular polynomial differential system with a nilpotent singularity ⋮ A new normal form for monodromic nilpotent singularities of planar vector fields ⋮ Nilpotent Global Centers of Linear Systems with Cubic Homogeneous Nonlinearities ⋮ Integrability and linearizability of cubic \(Z_2\) systems with non-resonant singular points ⋮ Simultaneity of centres in double-reversible planar differential systems

Uses Software

• primdec

Cites Work

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