Sections of Hamiltonian Systems
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.
Cite
@article{arxiv.2012.10169,
title = {Sections of Hamiltonian Systems},
author = {Konstantinos Kourliouros},
journal= {arXiv preprint arXiv:2012.10169},
year = {2021}
}