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Discrete time Bogoyavlensky lattices

Yu. B. Suris
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Abstract

Discretizations of the Bogoyavlensky lattices are introduced, belonging to the same hierarchies as the continuous--time systems. The construction exemplifies the general scheme for integrable discretization of systems on Lie algebras with $r$--matrix Poisson brackets. An initial value problem for the difference equations is solved in terms of a factorization problem in a group. Interpolating Hamiltonian flow is found.

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Yu. B. Suris. 1996-01-02. Discrete time Bogoyavlensky lattices. https://doi.org/10.1063/1.531611

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