Using discrete Darboux polynomials to detect and determine preserved measures and integrals of rational maps

DOI10.1088/1751-8121/ab294bzbMath1505.37074arXiv1902.04715OpenAlexW3101613243MaRDI QIDQ5055658

No author found.

Publication date: 9 December 2022

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1902.04715

zbMATH Keywords

Darboux polynomialsfirst integralsrational maps

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) 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) Computational methods for invariant manifolds of dynamical systems (37M21) Completely integrable discrete dynamical systems (37J70)

Related Items (9)

Coalgebra symmetry for discrete systems ⋮ Birational maps from polarization and the preservation of measure and integrals ⋮ On the preservation of second integrals by Runge-Kutta methods ⋮ Growth and integrability of some birational maps in dimension three ⋮ Geometric numerical integration. Abstracts from the workshop held March 28 -- April 3, 2021 (hybrid meeting) ⋮ Homogeneous Darboux polynomials and generalising integrable ODE systems ⋮ Detecting and determining preserved measures and integrals of birational maps ⋮ A Novel Integrable Fourth-Order Difference Equation Admitting Three Invariants ⋮ A novel 8-parameter integrable map in R⁴

Cites Work

• Unnamed Item
• Unnamed Item
• On integrability of Hirota-Kimura type discretizations
• Three-dimensional discrete systems of Hirota-Kimura type and deformed Lie-Poisson algebras
• Real topological entropy versus metric entropy for birational measure-preserving transformations
• Singularity, complexity, and quasi-integrability of rational mappings
• Discretization of the Lagrange Top
• Discretization of the Euler Top
• How to find the conserved quantities of nonlinear discrete equations
• Arithmetical Method to Detect Integrability in Maps
• Integrability properties of Kahanʼs method
• Splitting methods
• Duality for discrete integrable systems
• Duality for discrete integrable systems II
• A Darboux-type Theory of Integrability for Discrete Dynamical Systems
• Geometric properties of Kahan's method
• Closed-form expressions for integrals of traveling wave reductions of integrable lattice equations

This page was built for publication: Using discrete Darboux polynomials to detect and determine preserved measures and integrals of rational maps