The Optimal Momentum Map

  • Juan-Pablo Ortega
  • Tudor S. Ratiu


The presence of symmetries in a Hamiltonian system usually simplies the existence of conservation laws that are represented mathematically in terms of the dynamical preservation of the level sets of a momentum mapping. The symplectic or Marsden-Weinstein reduction procedure takes advantage of this and associates to the original system a new Hamiltonian system with fewer degrees of freedom. However, in a large number of situations, this standard approach does not work or is not e cient enough, in the sense that it does not use all the information encoded in the symmetry of the system. In this work, a new momentum map will be defined that is capable of overcoming most of the problems encountered in the traditional approach.


Hamiltonian System Poisson Bracket Symplectic Manifold Invariant Function Hamiltonian Vector 
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© Springer-Verlag New York, Inc. 2002

Authors and Affiliations

  • Juan-Pablo Ortega
  • Tudor S. Ratiu

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