Exact smooth classification of Hamiltonian vector fields on two-dimensional manifolds
type: Item
instance of: scholarly article
title: Exact smooth classification of Hamiltonian vector fields on two-dimensional manifolds
zbMATH Open document ID: 0919.58027
DOI: 10.1007/BF02355725
published in: Mathematical Notes
publication date: 1999-03-23T00:00:00Z
review text: The paper presents a complete trajectory classification of integrable Hamiltonian systems in general position with two degrees of freedom on isoenergetic surfaces in the category \(C^0\). The problem under consideration in many cases can be reduced to the exact classification (in the category \(C^0\)) of Hamiltonian systems in general position with one degree of freedom near a critical leaf of the foliation of the surface of the trajectories. A similar reduction is also feasible in the category of \(C^k\)-smooth maps. The classification imposes no restrictions on Morse functions.
Mathematics Subject Classification ID: 37J99
zbMATH DE Number: 1238008
zbMATH Keywords: two-dimensional manifold
zbMATH Keywords: germ
zbMATH Keywords: Morse function
author: Boris Kruglikov
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02355725
OpenAlex ID: W1991592227
description: scientific article; zbMATH DE number 1238008