Sections of Hamiltonian Systems

    2021, Volume 26, Number 4, pp.  331-349

    Author(s): Kourliouros K.

    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
    Citation: Kourliouros K., Sections of Hamiltonian Systems, Regular and Chaotic Dynamics, 2021, Volume 26, Number 4, pp. 331-349

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