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 …
Geometry of the Kahan discretizations of planar quadratic Hamiltonian systems. II. Systems with a linear Poisson tensor
M Petrera, YB Suris - arXiv preprint arXiv:1811.05791, 2018 - arxiv.org
Kahan discretization is applicable to any quadratic vector field and produces a birational
map which approximates the shift along the phase flow. For a planar quadratic Hamiltonian …
map which approximates the shift along the phase flow. For a planar quadratic Hamiltonian …
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 …
Discretization of the Lotka–Volterra System and Asymptotic Focal and Prefocal Sets
JP Françoise, D Fournier-Prunaret - International Journal of …, 2024 - World Scientific
We revisit the Kahan–Hirota–Kimura discretization of a quadratic vector field. The
corresponding discrete system is generated by successive iterations of a birational map F h …
corresponding discrete system is generated by successive iterations of a birational map F h …
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 …
Integrable boundary conditions for quad equations, open boundary reductions, and integrable mappings
V Caudrelier, PH van der Kamp… - International Mathematics …, 2022 - academic.oup.com
In the context of integrable difference equations on quad-graphs, we introduce the method of
open boundary reductions, as an alternative to the well-known periodic reductions, for …
open boundary reductions, as an alternative to the well-known periodic reductions, for …
A new class of integrable maps of the plane: Manin transformations with involution curves
PH van der Kamp - … . Symmetry, Integrability and Geometry: Methods and …, 2021 - emis.de
A New Class of Integrable Maps of the Plane: Manin Transformations with Involution Curves
Page 1 Symmetry, Integrability and Geometry: Methods and Applications SIGMA 17 (2021) …
Page 1 Symmetry, Integrability and Geometry: Methods and Applications SIGMA 17 (2021) …
[图书][B] Some aspects of integrability of birational maps
R Zander - 2021 - search.proquest.com
In dieser Arbeit behandeln wir verschiedene Aspekte zur Integrabilität von birationalen
Abbildungen, vorrangig im Kontext von Abbildungen, welche als Kahan-Diskretisierung von …
Abbildungen, vorrangig im Kontext von Abbildungen, welche als Kahan-Diskretisierung von …