Structurally stable quadratic vector fields

1998 ◽  
Vol 134 (639) ◽  
pp. 0-0 ◽  
Author(s):  
Joan C. Artés ◽  
Robert E. Kooij ◽  
Jaume Llibre
Keyword(s):  
Vector Fields ◽  
Quadratic Vector Fields ◽  
Structurally Stable

Nonexistence of limit cycles for a class of structurally stable quadratic vector fields

2007 ◽  
Vol 17 (2) ◽  
pp. 259-270 ◽  
Author(s):  
J. C. Artés ◽  
◽  
Jaume Llibre ◽  
J. C. Medrado ◽  
◽  
...  
Keyword(s):  
Limit Cycles ◽  
Vector Fields ◽  
Quadratic Vector Fields ◽  
Structurally Stable

scholarly journals On the singularity structure of Kahan discretizations of a class of quadratic vector fields

2021 ◽  
Author(s):  
René Zander
Keyword(s):  
Elliptic Curves ◽  
Vector Fields ◽  
Singularity Structure ◽  
Quadratic Vector Fields ◽  
Parameter Values

AbstractWe discuss the singularity structure of Kahan discretizations of a class of quadratic vector fields and provide a classification of the parameter values such that the corresponding Kahan map is integrable, in particular, admits an invariant pencil of elliptic curves.

Planar quadratic vector fields with finite saddle connection on a straight line (convex case)

2005 ◽  
Vol 6 (2) ◽  
pp. 187-204 ◽  
Author(s):  
Paulo César Carrião ◽  
Maria Elasir Seabra Gomes ◽  
Antonio Augusto Gaspar Ruas
Keyword(s):  
Vector Fields ◽  
Saddle Connection ◽  
Quadratic Vector Fields ◽  
Straight Line ◽  
Convex Case

Twelve Limit Cycles in 3D Quadratic Vector Fields with Z3 Symmetry

2018 ◽  
Vol 28 (11) ◽  
pp. 1850139 ◽  
Author(s):  
Laigang Guo ◽  
Pei Yu ◽  
Yufu Chen
Keyword(s):  
Limit Cycles ◽  
Vector Fields ◽  
Center Manifold ◽  
Three Dimensional ◽  
Center Manifold Theory ◽  
Normal Form Theory ◽  
Quadratic Vector Fields ◽  
Fine Focus ◽  
Form Theory ◽  
Manifold Theory

This paper is concerned with the number of limit cycles bifurcating in three-dimensional quadratic vector fields with [Formula: see text] symmetry. The system under consideration has three fine focus points which are symmetric about the [Formula: see text]-axis. Center manifold theory and normal form theory are applied to prove the existence of 12 limit cycles with [Formula: see text]–[Formula: see text]–[Formula: see text] distribution in the neighborhood of three singular points. This is a new lower bound on the number of limit cycles in three-dimensional quadratic systems.

scholarly journals Bistable vector fields are axiom A

1995 ◽  
Vol 51 (1) ◽  
pp. 83-86
Author(s):  
Mike Hurley
Keyword(s):  
Vector Field ◽  
Compact Manifold ◽  
Vector Fields ◽  
Axiom A ◽  
Smooth Compact Manifold ◽  
Structurally Stable

Recently L. Wen showed that if a C1 vector field (on a smooth compact manifold without boundary) is both structurally stable and topologically stable then it will satisfy Axiom A. The purpose of this note is to indicate how results from an earlier paper can be used to simplify somewhat Wen's argument.

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