Abstract:
A section of a Hamiltonian system is a hypersurface in the phase space of the
system, usually representing a set of one-sided constraints (e. g., a boundary, an obstacle or
a set of admissible states). In this paper we give local classification results for all typical
singularities of sections of regular (non-singular) Hamiltonian systems, a problem equivalent
to the classification of typical singularities of Hamiltonian systems with one-sided constraints.
In particular, we give a complete list of exact normal forms with functional invariants, and
we show how these are related/obtained by the symplectic classification of mappings with
prescribed (Whitney-type) singularities, naturally defined on the reduced phase space of the
Hamiltonian system.
Keywords:Hamiltonian systems, constraints, singularities, normal forms, functional moduli.
References