Topological invariants of Liouville integrable Hamiltonian systems
type: Item
instance of: scholarly article
title: Topological invariants of Liouville integrable Hamiltonian systems
zbMATH Open document ID: 0697.58021
DOI: 10.1007/BF01077420
author: A. T. Fomenko
publication date: 1988-01-01T00:00:00Z
review text: Let Q be a compact three-dimensional isoenergetic surface for a Hamiltonian system and f a second integral on Q. Then it is possible to construct a certain graph \(\Gamma\) (Q,f) (in the sense of graph theory). Using the graph \(\Gamma\) (Q,f), the author presents three topological invariants of Hamiltonian systems that are integrable in the sense of Liouville. The integrable cases are characterized by these invariants independently of the choice of second integral. The invariants permit us to classify the integrable systems up to topological equivalence. In addition, the isoenergetic surfaces of the integrable systems can be classified by these invariants. For some classical integrable systems the invariants are calculated.
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 37J35
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 70H05
zbMATH DE Number: 4143084
zbMATH Keywords: topological invariants of Hamiltonian systems
zbMATH Keywords: isoenergetic surfaces
zbMATH Keywords: integrable systems
MaRDI profile type: Publication
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published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 4143084