The Geometry of Quadratic Polynomial Differential Systems with a Finite and an Infinite Saddle-Node (C)

DOI10.1142/S0218127415300098zbMath1314.34062OpenAlexW4245198949WikidataQ115245948 ScholiaQ115245948MaRDI QIDQ5252707

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

Publication date: 3 June 2015

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

Full work available at URL: https://doi.org/10.1142/s0218127415300098

zbMATH Keywords

phase portraitsbifurcation diagramalgebraic invariantsquadratic differential systemsfinite saddle-nodeinfinite saddle-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) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07)

Related Items (7)

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 \(\mathrm{QSH(D)}\) ⋮ Topological Classification of Quadratic Polynomial Differential Systems with a Finite Semi-Elemental Triple Saddle ⋮ 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)

Cites Work

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• GLOBAL PHASE PORTRAITS OF QUADRATIC POLYNOMIAL DIFFERENTIAL SYSTEMS WITH A SEMI-ELEMENTAL TRIPLE NODE
• The Geometry of Quadratic Polynomial Differential Systems with a Finite and an Infinite Saddle-Node (A, B)
• 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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