New classes of quadratic vector fields admitting integral-preserving Kahan-Hirota-Kimura discretizations

Abstract

We present some new families of quadratic vector fields, not necessarily integrable, for which their Kahan-Hirota-Kimura discretization exhibits the preservation of some of the characterizing features of the underlying continuous systems (conserved quantities and invariant measures).

arXiv comment12 pages

References in corpus (7)

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• Integrability properties of Kahan's method
• Discretization of polynomial vector fields by polarization
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Cited by in corpus (7)

• Manin involutions for elliptic pencils and discrete integrable systems
• On the singularity structure of Kahan discretizations of a class of quadratic vector fields
• Lax pairs for the discrete reduced Nahm systems
• An Elementary Construction of Modified Hamiltonians and Modified Measures of 2D Kahan Maps
• How one can repair non-integrable Kahan discretizations. II. A planar system with invariant curves of degree 6
• Explicit isomorphisms for the symmetry algebras of continuous and discrete isotropic oscillators
• Kahan-Hirota-Kimura maps preserving original cubic hamiltonians