How one can repair non-integrable Kahan discretizations. II: A planar system with invariant curves of degree 6
DOI10.1007/s11040-021-09413-2zbMath1485.37063arXiv2106.14301OpenAlexW3217628809MaRDI QIDQ2059037
Misha Schmalian, Yuriy Tumarkin, Yuri Borisovich Suris
Publication date: 13 December 2021
Published in: Mathematical Physics, Analysis and Geometry (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2106.14301
integrable discretizationbirational mapsdiscrete integrable systemsrational elliptic surfaceelliptic pencil
Relationships between algebraic curves and integrable systems (14H70) 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)
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Cites Work
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- On integrability of Hirota-Kimura type discretizations
- Manin involutions for elliptic pencils and discrete integrable systems
- An unconventional symplectic integrator of W. Kahan
- The problem of integrable discretization: Hamiltonian approach
- Algebraic entropy
- Integrable mappings and soliton equations. II
- Generalised Manin transformations and QRT maps
- On the singularity structure of Kahan discretizations of a class of quadratic vector fields
- Cremona transformations, surface automorphisms, and plain cubics. With an appendix by Igor Dolgachev
- Geometry of the Kahan discretizations of planar quadratic Hamiltonian systems. II: Systems with a linear Poisson tensor
- Analogues of Kahan's method for higher order equations of higher degree
- Discretization of the Lagrange Top
- Discretization of the Euler Top
- Dynamics of bimeromorphic maps of surfaces
- Nonlinear Partial Difference Equations. I. A Difference Analogue of the Korteweg-de Vries Equation
- Nonlinear Partial Difference Equations. II. Discrete-Time Toda Equation
- Nonlinear Partial Difference Equations III; Discrete Sine-Gordon Equation
- Nonlinear Partial Difference Equations. IV. Bäcklund Transformation for the Discrete-Time Toda Equation
- Integrability properties of Kahanʼs method
- On the Hamiltonian structure of Hirota-Kimura discretization of the Euler top
- On Integrability of Hirota–Kimura-Type Discretizations: Experimental Study of the Discrete Clebsch System
- Dynamics of birational maps of P^2
- A construction of a large family of commuting pairs of integrable symplectic birational four-dimensional maps
- Symmetric monopoles
- Geometric properties of Kahan's method
- Geometry of the Kahan discretizations of planar quadratic Hamiltonian systems
- On the Construction of Elliptic Solutions of Integrable Birational Maps
- 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
- Discretization of polynomial vector fields by polarization
- How one can repair non-integrable Kahan discretizations
- A novel 8-parameter integrable map in R4
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