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

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

We 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.

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Veröffentlicht in:European journal of mathematics 2021-09, Vol.7 (3), p.1046-1073
1. Verfasser: Zander, René
Format: Artikel
Sprache:eng
Schlagworte:
Algebraic Geometry
Curves
Discretization
Fields (mathematics)
Mathematics
Mathematics and Statistics
Research Article
Singularities
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Beschreibung
Zusammenfassung:We 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.
ISSN:2199-675X
2199-6768
DOI:10.1007/s40879-021-00479-4