Concepedia

LIE–TROTTER FORMULA AND POISSON DYNAMICS

International Journal of Bifurcation and Chaos · 1999 · 20 citations · 5 references

Concepts

Free Rigid BodyIntegrable SystemRigid BodyExplicit Poisson IntegratorsLie TheoryHamiltonian System

Abstract

We construct via the Lie–Trotter formula some explicit Poisson integrators for the Maxwell–Bloch equations from laser-matter dynamics, the Euler equations of the free rigid body and the equations of the rigid body with a spinning rotor.

References

5

On the product of semi-groups of operators

H. F. Trotter · Proceedings of the American Mathematical Society · 1959 · 2K citations · Full text

Topological Semigroups, Transformation Semigroups, Nilpotent Group +1

Symplectic maps for the n-body problem

Jack Wisdom, Matthew J. Holman · The Astronomical Journal · 1991 · 1.2K citations

Hamiltonian Theory, Orbit Determination, Symplectic Maps +10

Symplectic integrators for Hamiltonian problems: an overview

J. M. Sanz‐Serna · Acta Numerica · 1992 · 384 citations

Numerical Analysis, Applied Mathematical Modelling, Hamiltonian Theory +6

On the Numerical Integration of Ordinary Differential Equations by Symmetric Composition Methods

Robert I. McLachlan · SIAM Journal on Scientific Computing · 1995 · 360 citations

Numerical Analysis, Method Of Fundamental Solution, Numerical Computation +12

Explicit Lie-Poisson integration and the Euler equations

Robert I. McLachlan · Physical Review Letters · 1993 · 122 citations · Full text

Spectral Theory, Explicit Lie-poisson Integration, Lie-poisson Integrators +8