Qualitative classification of singular points

DOI10.1007/BF02972669zbMath1131.34304MaRDI QIDQ996114

Jaume Llibre, Qibao Jiang

Publication date: 11 September 2007

Published in: Qualitative Theory of Dynamical Systems (Search for Journal in Brave)

zbMATH Keywords

singular pointslocal phase portraitplanar systemanalytic vector fieldblowing-up

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems (37C15) Equivalence and asymptotic equivalence of ordinary differential equations (34C41)

Related Items (12)

Structurally unstable quadratic vector fields of codimension two: families possessing one finite saddle-node and a separatrix connection ⋮ Algebraic invariants and local stability of planar differential systems ⋮ A generalization of the Poincaré compactification and the real Jacobian conjecture ⋮ On the evolution of invariant Riemannian metrics on one class of generalized Wallach spaces under the influence of the normalized Ricci flow ⋮ Geometric configurations of singularities for quadratic differential systems with three distinct real simple finite singularities ⋮ Semi-invariants and their use for stability analysis of planar systems ⋮ Global configurations of singularities for quadratic differential systems with total finite multiplicity three and at most two real singularities ⋮ Darboux integrability and reversible quadratic vector fields ⋮ Stability analysis of planar systems with nilpotent (non-zero) linear part ⋮ A sufficient condition for the real Jacobian conjecture in \(\mathbb{R}^2\) ⋮ From topological to geometric equivalence in the classification of singularities at infinity for quadratic vector fields ⋮ The dynamics of the Ricci flow on generalized Wallach spaces

Cites Work

• Separatrices at singular points of planar vector fields
• High order Melnikov functions and the problem of uniformity in global bifurcation
• Dynamical systems I. Ordinary differential equations and smooth dynamical systems. Transl. from the Russian
• Singularities of vector fields on the plane
• Investigation of the behaviour of the integral curves of a system of two differential equations in the neighbourhood of a singular point
• Holonomie et intégrales premières
• Classification of Continuous Flows on 2-Manifolds
• Reduction of Singularities of the Differential Equation Ady = Bdx
• Global Structure of Ordinary Differential Equations in the Plane
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