Analytic integrability around a nilpotent singularity

DOI10.1016/j.jde.2019.01.015zbMath1432.34002arXiv1805.01726OpenAlexW2962791000MaRDI QIDQ1737543

Antonio Algaba, Jaume Giné, Cristóbal García

Publication date: 23 April 2019

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1805.01726

zbMATH Keywords

nilpotent singularityanalytic integrability

Mathematics Subject Classification ID

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) Symmetries, invariants of ordinary differential equations (34C14) Explicit solutions, first integrals of ordinary differential equations (34A05)

Related Items (11)

Algebraic integrability of nilpotent planar vector fields ⋮ Monodromic nilpotent singular points with odd Andreev number and the center problem ⋮ Normal forms of double Hopf oscillators with radial nonlinearities ⋮ Analytically integrable system orbitally equivalent to a semi-quasihomogeneous system ⋮ Integrability of planar nilpotent differential systems through the existence of an inverse integrating factor ⋮ Analytical integrability of perturbations of quadratic systems ⋮ On the integrability problem for the Hopf-zero singularity and its relation with the inverse Jacobi multiplier ⋮ Orbital normal forms for a class of three-dimensional systems with an application to Hopf-zero bifurcation analysis of Fitzhugh-Nagumo system ⋮ Analytically integrable centers of perturbations of cubic homogeneous systems ⋮ Bifurcation control and sound intensities in musical art ⋮ A new normal form for monodromic nilpotent singularities of planar vector fields

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