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Sbornik: Mathematics, 2010, Volume 201, Issue 8, Pages 1153–1191
DOI: https://doi.org/10.1070/SM2010v201n08ABEH004108 (Mi sm7654) 		 
This article is cited in 16 scientific papers (total in 16 papers)

Classification of hyperbolic singularities of rank zero of integrable Hamiltonian systems

A. A. Oshemkov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
English version PDF (545 kB) Citations (16)
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DOI: https://doi.org/10.1070/SM2010v201n08ABEH004108
Abstract: A complete invariant is constructed that is a solution of the problem of semilocal classification of saddle singularities of integrable Hamiltonian systems. Namely, a certain combinatorial object (an $f_n$-graph) is associated with every nondegenerate saddle singularity of rank zero; as a result, the problem of semilocal classification of saddle singularities of rank zero is reduced to the problem of enumeration of the $f_n$-graphs. This enables us to describe a simple algorithm for obtaining the lists of saddle singularities of rank zero for a given number of degrees of freedom and a given complexity.
Bibliography: 24 titles.
Keywords: integrable Hamiltonian systems, the momentum map, nondegenerate singularities, topological invariants.
Received: 18.11.2009
Russian version:
Matematicheskii Sbornik, 2010, Volume 201, Number 8, Pages 63–102
DOI: https://doi.org/10.4213/sm7654
Bibliographic databases:
Document Type: Article
UDC: 517.938.5+515.164.15
MSC: Primary 37J35; Secondary 37J05, 37J15, 57R45, 58K45, 70G40
Language: English
Original paper language: Russian
Citation: A. A. Oshemkov, “Classification of hyperbolic singularities of rank zero of integrable Hamiltonian systems”, Mat. Sb., 201:8 (2010), 63–102; Sb. Math., 201:8 (2010), 1153–1191
Citation in format AMSBIB
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    • This publication is cited in the following 16 articles:
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