Generators of groups of Hamitonian maps

TL;DR

This paper demonstrates that analytic Hamiltonian systems in various settings can be approximated by compositions of simple shear maps, each depending solely on position or momentum, simplifying their analysis.

Contribution

It introduces a novel approximation technique for Hamiltonian dynamics using compositions of nonlinear shear maps depending on a single variable.

Findings

Hamiltonian dynamics can be approximated by shear maps

The approximation applies to tori, annuli, and Euclidean space

Simplifies the study of Hamiltonian systems

Abstract

We prove that analytic Hamiltonian dynamics on tori, annuli, or Euclidean space can be approximated by a composition of nonlinear shear maps where each of the shears depends only on the position or only on the momentum.