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1 results

  • Differential Structure of Orbit Spaces

  • Richard Cushman, Jędrzej Śniatycki
  • Journal:
    Canadian Journal of Mathematics / Volume 53 / Issue 4 / 01 August 2001
    Published online by Cambridge University Press:
    20 November 2018, pp. 715-755
    Print publication:
    01 August 2001
    • Article
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  • We present a new approach to singular reduction of Hamiltonian systems with symmetries. The tools we use are the category of differential spaces of Sikorski and the Stefan-Sussmann theorem. The former is applied to analyze the differential structure of the spaces involved and the latter is used to prove that some of these spaces are smooth manifolds.

    Our main result is the identification of accessible sets of the generalized distribution spanned by the Hamiltonian vector fields of invariant functions with singular reduced spaces. We are also able to describe the differential structure of a singular reduced space corresponding to a coadjoint orbit which need not be locally closed.