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

Abstract

We discuss the singularity structure of Kahan discretizations of a class of quadratric 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.

arXiv comment19 pages, 4 figures, some minor changes

References in corpus (9)

• Symetric Monopoles
• Geometric properties of Kahan's method
• Symmetric Monopoles
• On integrability of Hirota-Kimura type discretizations
• Integrability properties of Kahan's method
• Transformations birationnelles de petit degré
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• New classes of quadratic vector fields admitting integral-preserving Kahan-Hirota-Kimura discretizations

Cited by in corpus (3)

• Manin involutions for elliptic pencils and discrete integrable systems
• How one can repair non-integrable Kahan discretizations. II. A planar system with invariant curves of degree 6
• Space of initial values of a map with a quartic invariant