Sections of Hamiltonian Systems

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