Advertisement

Neumann’s dynamical system

  • David Mumford
Part of the Modern Birkhäuser Classics book series (MBC)

Abstract

In classical mechanics, one encounters the class of problems: M = real 2n-dimensional manifold, with a closed non-degenerate differential 2-form ω
$$ \hat \omega = {\text{dual skew - symmetric form on T}}_{\text{M}}^{\text{*}} $$
$$ {\rm H} = e^\infty - {\text{function on M, called the Hamiltonian}}{\text{.}} $$
$$ {\rm X}_{\rm H} = \left\{ {\begin{array}{*{20}c} {the vector field on M defined by} \\ {\omega \left( {{\rm X}_{\rm H} ,Y} \right) = \left\langle {Y,dH} \right\rangle for all vectors Y} \\ {or} \\ {\hat \omega \left( {dH,\alpha } \right) = \left\langle {{\rm X}_{\rm H} ,\alpha } \right\rangle for all 1 - forms \alpha } \\ \end{array} } \right\} $$

Keywords

Vector Field Poisson Bracket Abelian Variety Symplectic Structure Cotangent Bundle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Birkhäuser Boston 2007

Authors and Affiliations

  • David Mumford
    • 1
  1. 1.Division of Applied MathematicsBrown UniversityProvidenceUSA

Personalised recommendations