Three classes of quadratic vector fields for which the Kahan discretization is the root of a generalised Manin transformation
Exactly Solvable and Integrable Systems
2018-06-18 v1
Abstract
We apply Kahan's discretisation method to three classes of 2-dimensional quadratic vector fields with quadratic, resp cubic, resp quartic Hamiltonians. We show that the maps obtained in this way can be geometrically understood as the composition of two involutions, one of which is a (linear) symmetry switch, and the other is a generalised Manin involution.
Keywords
Cite
@article{arxiv.1806.05917,
title = {Three classes of quadratic vector fields for which the Kahan discretization is the root of a generalised Manin transformation},
author = {Peter H. van der Kamp and Elena Celledoni and Robert I. McLachlan and David I. McLaren and Brynjulf Owren and G. R. W. Quispel},
journal= {arXiv preprint arXiv:1806.05917},
year = {2018}
}
Comments
7 pages, 3 figures