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.

19 pages, 4 figures, some minor changes

References in corpus (2)

• Geometry of the Kahan discretizations of planar quadratic Hamiltonian systems
• Singularity confinement as an integrability criterion

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