• Corpus ID: 225428174

Algebraic discretization of time-independent Hamiltonian systems using a Lie-group/algebra approach.

  title={Algebraic discretization of time-independent Hamiltonian systems using a Lie-group/algebra approach.},
  author={S Bertrand},
  journal={arXiv: Mathematical Physics},
  • S. Bertrand
  • Published 7 August 2020
  • Mathematics
  • arXiv: Mathematical Physics
In this paper, time-independent Hamiltonian systems are investigated via a Lie-group/algebra formalism. The (unknown) solution linked with the Hamiltonian is considered to be a Lie-group transformation of the initial data, where the group parameter acts as the time. The time-evolution generator (i.e. the Lie algebra associated to the group transformation) is constructed at an algebraic level, hence avoiding discretization of the time-derivatives for the discrete case. This formalism makes it… 

Figures from this paper


On rotationally invariant integrable and superintegrable classical systems in magnetic fields with non-subgroup type integrals
The aim of the present article is to construct quadratically integrable three dimensional systems in non-vanishing magnetic fields which possess so-called non-subgroup type integrals. The presence of
Classical and quantum superintegrability with applications
A superintegrable system is, roughly speaking, a system that allows more integrals of motion than degrees of freedom. This review is devoted to finite dimensional classical and quantum
Symmetries and Integrability of Difference Equations
The notion of integrability was first introduced in the 19th century in the context of classical mechanics with the definition of Liouville integrability for Hamiltonian flows. Since then, several
Three-dimensional superintegrable systems in a static electromagnetic field
We consider a charged particle moving in a static electromagnetic field described by the vector potential $\vec A(\vec x)$ and the electrostatic potential $V(\vec x)$. We study the conditions on the
Geometric Integration via Multi-space
The method of invariantization is based on the equivariant moving frame theory applied to prolonged symmetry group actions on multi-space, which has been proposed as the proper geometric setting for numerical analysis.
On integrability aspects of the supersymmetric sine-Gordon equation
In this paper we study certain integrability properties of the supersymmetric sine-Gordon equation. We construct Lax pairs with their zero-curvature representations which are equivalent to the
On the development of symmetry-preserving finite element schemes for ordinary differential equations
In this paper we introduce a procedure, based on the method of equivariant moving frames, for formulating continuous Galerkin finite element schemes that preserve the Lie point symmetries of initial
Symmetry-Preserving Numerical Schemes
In these lectures we review two procedures for constructing finite difference numerical schemes that preserve symmetries of differential equations. The first approach is based on Lie’s infinitesimal
The discretized Boussinesq equation and its conditional symmetry reduction
In this article we show that we can carry out the symmetry preserving discretization of the Boussinesq equation with respect to three of its more significant conditional symmetries. We perform the