Poisson brackets of mappings obtained as (q,-p) reductions of lattice equations

TL;DR

This paper derives Poisson brackets for mappings from integrable lattice equations' periodic reductions using Ostrogradsky transformation, advancing understanding of their Hamiltonian structures.

Contribution

It introduces a method to compute Poisson brackets for mappings from lattice equations via Ostrogradsky transformation, providing new insights into their integrable structure.

Findings

Poisson brackets are explicitly derived for certain lattice reductions.

The method applies Ostrogradsky transformation to obtain Hamiltonian structures.

Results contribute to the theory of integrable mappings and their algebraic properties.

Abstract

In this paper, we present Poisson brackets of certain classes of mappings obtained as general periodic reductions of integrable lattice equations. The Poisson brackets are derived using the so called Ostrogradsky transformation.