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Sections of Hamiltonian Systems

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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.

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Funding

This research was supported by the São Paulo Research Foundation, FAPESP [grant number: 2017/23555-9].

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  1. ICMC-USP, Av. Trabalhador Sancarlense 400-Centro, 13566-590, São Carlos, SP, Brasil

    Konstantinos Kourliouros

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  1. Konstantinos Kourliouros
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Correspondence to Konstantinos Kourliouros.

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The authors declare that they have no conflicts of interest.

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MSC2010

34C20, 37J06, 57R45, 70H15, 70H45

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Kourliouros, K. Sections of Hamiltonian Systems. Regul. Chaot. Dyn. 26, 331–349 (2021). https://doi.org/10.1134/S156035472104002X

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  • DOI: https://doi.org/10.1134/S156035472104002X

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