Birational maps from polarization and the preservation of measure and integrals
DOI10.1088/1751-8121/acee31zbMath1525.37073arXiv2303.04300MaRDI QIDQ6095272
Robert I. Mclachlan, David I. McLaren, Gilles Reinout Willem Quispel
Publication date: 7 September 2023
Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2303.04300
Rational and birational maps (14E05) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15) Integrable difference and lattice equations; integrability tests (39A36) Completely integrable discrete dynamical systems (37J70)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- On integrability of Hirota-Kimura type discretizations
- B-series methods are exactly the affine equivariant methods
- Lax pairs for the discrete reduced Nahm systems
- An unconventional symplectic integrator of W. Kahan
- Unconventional schemes for a class of ordinary differential equations - with applications to the Korteweg-de Vries equation
- A coordinate-free reduction for flows on the volume manifold
- Singularity, complexity, and quasi-integrability of rational mappings
- Detecting and determining preserved measures and integrals of birational maps
- Analogues of Kahan's method for higher order equations of higher degree
- Discretization of the Lagrange Top
- Discretization of the Euler Top
- Integrable mappings of the plane preserving biquadratic invariant curves
- Integrability properties of Kahanʼs method
- Liouville integrability and superintegrability of a generalized Lotka–Volterra system and its Kahan discretization
- Splitting methods
- On Integrability of Hirota–Kimura-Type Discretizations: Experimental Study of the Discrete Clebsch System
- A Darboux-type Theory of Integrability for Discrete Dynamical Systems
- Geometric properties of Kahan's method
- Using discrete Darboux polynomials to detect and determine preserved measures and integrals of rational maps
- A Hamilton–Jacobi formalism for higher order implicit Lagrangians
- Bi-rational maps in four dimensions with two invariants
- The Cremona group
- Three classes of quadratic vector fields for which the Kahan discretisation is the root of a generalised Manin transformation
- Geometric and integrability properties of Kahan’s method: the preservation of certain quadratic integrals
- New classes of quadratic vector fields admitting integral-preserving Kahan–Hirota–Kimura discretizations
- Conservative Methods for Dynamical Systems
- Integrable and superintegrable systems associated with multi-sums of products
- Discretization of polynomial vector fields by polarization
- A novel 8-parameter integrable map in R4
This page was built for publication: Birational maps from polarization and the preservation of measure and integrals
