GLOBAL PHASE PORTRAITS OF QUADRATIC POLYNOMIAL DIFFERENTIAL SYSTEMS WITH A SEMI-ELEMENTAL TRIPLE NODE

DOI10.1142/S021812741350140XzbMath1275.34045arXiv1212.6645OpenAlexW3099453737MaRDI QIDQ2864975

Joan C. Artés, Alex Rezende, Regilene D. S. Oliveira

Publication date: 27 November 2013

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1212.6645

zbMATH Keywords

phase portraitsbifurcation diagramalgebraic invariantsquadratic differential systemssemi-elemental triple node

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Symmetries, invariants of ordinary differential equations (34C14) Bifurcation theory for ordinary differential equations (34C23) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (10)

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 ⋮ Structurally unstable quadratic vector fields of codimension two: families possessing one finite saddle-node and a separatrix connection ⋮ The interplay among the topological bifurcation diagram, integrability and geometry for the family \(\mathrm{QSH(D)}\) ⋮ Phase portraits of planar piecewise linear refracting systems: focus-saddle case ⋮ Topological Classification of Quadratic Polynomial Differential Systems with a Finite Semi-Elemental Triple Saddle ⋮ The Geometry of Quadratic Polynomial Differential Systems with a Finite and an Infinite Saddle-Node (C) ⋮ Quadratic Differential Systems with a Finite Saddle-Node and an Infinite Saddle-Node (1,1)SN - (A) ⋮ Quadratic Differential Systems with a Finite Saddle-Node and an Infinite Saddle-Node (1, 1)SN - (B) ⋮ GLOBAL PHASE PORTRAITS OF SOME REVERSIBLE CUBIC CENTERS WITH NONCOLLINEAR SINGULARITIES

Cites Work

• Characterization of the finite weak singularities of quadratic systems via invariant theory
• Hilbert's 16th problem for quadratic vector fields
• On the geometric structure of the class of planar quadratic differential systems.
• Geometry of quadratic differential systems in the neighborhood of infinity
• A survey of quadratic systems
• SINGULAR POINTS OF QUADRATIC SYSTEMS: A COMPLETE CLASSIFICATION IN THE COEFFICIENT SPACE ℝ¹²
• The Geometry of Quadratic Differential Systems with a Weak Focus of Third Order
• THE GEOMETRY OF QUADRATIC DIFFERENTIAL SYSTEMS WITH A WEAK FOCUS OF SECOND ORDER
• On the geometry in the neighbourhood of infinity of quadratic differential systems with a weak focus

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