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 Clifford algebra-based structure filtering analysis for geophysical vector fields

2013 ◽  
Vol 20 (4) ◽  
pp. 563-570 ◽  
Author(s):  
Z. Yu ◽  
W. Luo ◽  
L. Yi ◽  
Y. Hu ◽  
L. Yuan
Keyword(s):  
Vector Field ◽  
Clifford Algebra ◽  
El Niño ◽  
Vector Fields ◽  
El Nino ◽  
Field Analysis ◽  
Directional Information ◽  
Filtering Method ◽  
Additional Information

Abstract. A new Clifford algebra-based vector field filtering method, which combines amplitude similarity and direction difference synchronously, is proposed. Firstly, a modified correlation product is defined by combining the amplitude similarity and direction difference. Then, a structure filtering algorithm is constructed based on the modified correlation product. With custom template and thresholds applied to the modulus and directional fields independently, our approach can reveal not only the modulus similarities but also the classification of the angular distribution. Experiments on exploring the tempo-spatial evolution of the 2002–2003 El Niño from the global wind data field are used to test the algorithm. The results suggest that both the modulus similarity and directional information given by our approach can reveal the different stages and dominate factors of the process of the El Niño evolution. Additional information such as the directional stability of the El Niño can also be extracted. All the above suggest our method can provide a new powerful and applicable tool for geophysical vector field analysis.

scholarly journals On the symmetries of three-dimensional generalized symmetric spaces

2021 ◽  
Vol 13(62) (2) ◽  
pp. 451-462
Author(s):  
Lakehal Belarbi
Keyword(s):  
Symmetric Spaces ◽  
Vector Fields ◽  
Killing Vector ◽  
Three Dimensional ◽  
Riemannian Metric ◽  
Killing Vector Fields ◽  
Generalized Symmetric Space ◽  
Generalized Symmetric Spaces ◽  
Full Classification

In this work we consider the three-dimensional generalized symmetric space, equipped with the left-invariant pseudo-Riemannian metric. We determine Killing vector fields and affine vectors fields. Also we obtain a full classification of Ricci, curvature and matter collineations

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
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