From topological to geometric equivalence in the classification of singularities at infinity for quadratic vector fields

DOI10.1216/RMJ-2015-45-1-29zbMath1318.34045MaRDI QIDQ2340831

Nicolae Vulpe, Joan C. Artés, Jaume Llibre, Dana Schlomiuk

Publication date: 21 April 2015

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.rmjm/1428412773

zbMATH Keywords

Poincaré compactificationquadratic vector fieldsconfiguration of singularitiesaffine invariant polynomials of singularityinfinite singularities

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Singularities of vector fields, topological aspects (58K45) Equivalence and asymptotic equivalence of ordinary differential equations (34C41)

Related Items (12)

Quadratic systems with an invariant conic having Darboux invariants ⋮ Structurally unstable quadratic vector fields of codimension two: families possessing either a cusp point or two finite saddle-nodes ⋮ Phase portraits of separable quadratic systems and a bibliographical survey on quadratic systems ⋮ Unnamed Item ⋮ Plane polynomials and Hamiltonian vector fields determined by their singular points ⋮ Qualitative dynamics of five quadratic polynomial differential systems exhibiting five classical cubic algebraic curves ⋮ Geometric configurations of singularities for quadratic differential systems with three distinct real simple finite singularities ⋮ Phase portraits of random planar homogeneous vector fields ⋮ Global configurations of singularities for quadratic differential systems with total finite multiplicity three and at most two real singularities ⋮ Invariant conditions for phase portraits of quadratic systems with complex conjugate invariant lines meeting at a finite point ⋮ Topological Classification of Quadratic Polynomial Differential Systems with a Finite Semi-Elemental Triple Saddle ⋮ On families \(\boldsymbol{QSL}_{\geq 2}\) of quadratic systems with invariant lines of total multiplicity at least 2

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