Manin involutions for elliptic pencils and discrete integrable systems
M Petrera, YB Suris, K Wei, R Zander - Mathematical Physics, Analysis and …, 2021 - Springer
We contribute to the algebraic-geometric study of discrete integrable systems generated by
planar birational maps:(a) we find geometric description of Manin involutions for elliptic …
planar birational maps:(a) we find geometric description of Manin involutions for elliptic …
Three classes of quadratic vector fields for which the Kahan discretisation is the root of a generalised Manin transformation
PH Van der Kamp, E Celledoni… - Journal of Physics A …, 2019 - iopscience.iop.org
We apply Kahan's discretisation method to three classes of 2D quadratic vector fields with
quadratic, resp. cubic, resp. quartic Hamiltonians. We show that the maps obtained in this …
quadratic, resp. cubic, resp. quartic Hamiltonians. We show that the maps obtained in this …
New classes of quadratic vector fields admitting integral-preserving Kahan–Hirota–Kimura discretizations
M Petrera, R Zander - Journal of Physics A: Mathematical and …, 2017 - iopscience.iop.org
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 …
which their Kahan–Hirota–Kimura discretization exhibits the preservation of some of the …
Determination of the symmetry group for some QRT roots
G Gubbiotti, Y Shi - arXiv preprint arXiv:2305.17107, 2023 - arxiv.org
We determine the affine Weyl symmetries of some two-dimensional birational maps known
as QRT roots arising from Kahan--Hirota--Kimura discretisation of two different reduced …
as QRT roots arising from Kahan--Hirota--Kimura discretisation of two different reduced …
How one can repair non-integrable Kahan discretizations
M Petrera, YB Suris, R Zander - arXiv preprint arXiv:2003.12596, 2020 - arxiv.org
Kahan discretization is applicable to any system of ordinary differential equations on
$\mathbb R^ n $ with a quadratic vector field, $\dot {x}= f (x)= Q (x)+ Bx+ c $, and produces a …
$\mathbb R^ n $ with a quadratic vector field, $\dot {x}= f (x)= Q (x)+ Bx+ c $, and produces a …
On the singularity structure of Kahan discretizations of a class of quadratic vector fields
R Zander - European Journal of Mathematics, 2021 - Springer
On the singularity structure of Kahan discretizations of a class of quadratic vector fields |
European Journal of Mathematics Skip to main content SpringerLink Log in Menu Find a journal …
European Journal of Mathematics Skip to main content SpringerLink Log in Menu Find a journal …
Generalised Manin transformations and QRT maps
PH van der Kamp, DI McLaren… - arXiv preprint arXiv …, 2018 - arxiv.org
Manin transformations are maps of the plane that preserve a pencil of cubic curves. They are
the composition of two involutions. Each involution is constructed in terms of an involution …
the composition of two involutions. Each involution is constructed in terms of an involution …
Lax pairs for the discrete reduced Nahm systems
G Gubbiotti - Mathematical Physics, Analysis and Geometry, 2021 - Springer
We discretise the Lax pair for the reduced Nahm systems and prove its equivalence with the
Kahan–Hirota–Kimura discretisation procedure. We show that these Lax pairs guarantee the …
Kahan–Hirota–Kimura discretisation procedure. We show that these Lax pairs guarantee the …
How one can repair non-integrable Kahan discretizations. II. A planar system with invariant curves of degree 6
M Schmalian, YB Suris, Y Tumarkin - Mathematical Physics, Analysis and …, 2021 - Springer
We find a novel one-parameter family of integrable quadratic Cremona maps of the plane
preserving a pencil of curves of degree 6 and of genus 1. They turn out to serve as Kahan …
preserving a pencil of curves of degree 6 and of genus 1. They turn out to serve as Kahan …
An elementary construction of modified Hamiltonians and modified measures of 2D Kahan maps
G Gubbiotti, D McLaren… - Open Communications in …, 2024 - ocnmp.episciences.org
We show how to construct in an elementary way the invariant of the KHK discretisation of a
cubic Hamiltonian system in two dimensions. That is, we show that this invariant is …
cubic Hamiltonian system in two dimensions. That is, we show that this invariant is …