Discrete time Bogoyavlensky lattices

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.

22 pages, LaTeX, revised version (the third lattice discretized now!)

References in corpus (4)

• Integrable Time-Discretisation of the Ruijsenaars-Schneider Model
• A discrete time relativistic Toda lattice
• A time-discretized version of the Calogero-Moser model
• Dynamical R-Matrices for Integrable Maps

Cited by in corpus (9)

• Algebraic Structure of Discrete Zero Curvature Equations and Master Symmetries of Discrete Evolution Equations
• A note on the integrable discretization of the nonlinear Schrödinger equation
• What is the relativistic Volterra lattice?
• On discrete integrable equations of higher order
• On an integrable discretization of the modified Korteweg-de Vries equation
• Integrable discretizations of the spin Ruijsenaars-Schneider models
• Integrable discrete autonomous quad-equations admitting, as generalized symmetries, known five-point differential-difference equations
• Integrable discretizations for lattice systems: local equations of motion and their Hamiltonian properties
• On generalized Lotka-Volterra lattices