Generators of groups of Hamitonian maps
Pierre Berger, Dmitry Turaev

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.
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Taxonomy
TopicsNonlinear Waves and Solitons · Homotopy and Cohomology in Algebraic Topology · Geometric Analysis and Curvature Flows
