On the Construction of Elliptic Solutions of Integrable Birational Maps

DOI10.1080/10586458.2016.1166354zbMath1380.37116OpenAlexW3100106288MaRDI QIDQ4976187

Yuri N. Fedorov, Andreas Pfadler, Matteo Petrera, Yuri Borisovich Suris

Publication date: 27 July 2017

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/2117/105045

zbMATH Keywords

elliptic functionsbirational mapintegrable map

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Relationships between algebraic curves and integrable systems (14H70) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Entire and meromorphic solutions to ordinary differential equations in the complex domain (34M05) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Elliptic functions and integrals (33E05)

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Cites Work

• Unnamed Item
• On integrability of Hirota-Kimura type discretizations
• Three-dimensional discrete systems of Hirota-Kimura type and deformed Lie-Poisson algebras
• On an explicitly soluble system of nonlinear differential equations related to certain Toda lattices
• A note on the averaging for single-phase elliptic solutions of the Toda and the Volterra lattices
• Discretization of the Lagrange Top
• Discretization of the Euler Top
• 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
• Geometric properties of Kahan's method