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Discrete-time analogues of some nonlinear oscillators in the inverse-square potential. (English) Zbl 0840.70018

Summary: We propose a family of symplectic maps providing finite difference approximations for the Wojciechowski and Rosochatius systems. The Lax pair representations are found and complete integrability is proved.

MSC:

70H05 Hamilton’s equations
37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
35Q99 Partial differential equations of mathematical physics and other areas of application
39A12 Discrete version of topics in analysis
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