Classification of hyperbolic singularities of rank zero of integrable Hamiltonian systems

Journal Article · Wed Oct 06 00:00:00 EDT 2010 · Sbornik. Mathematics

DOI:https://doi.org/10.1070/SM2010V201N08ABEH004108· OSTI ID:21418073

Oshemkov, Andrey A ^[1]

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1. M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)

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{sub 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{sub 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.

• OSTI ID: 21418073
• Journal Information: Sbornik. Mathematics, Vol. 201, Issue 8; Other Information: DOI: 10.1070/SM2010v201n08ABEH004108; ISSN 1064-5616
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
ALGORITHMS
BIBLIOGRAPHIES
CLASSIFICATION
DEGREES OF FREEDOM
HAMILTONIANS
INTEGRAL CALCULUS
MATHEMATICAL SOLUTIONS
SINGULARITY
DOCUMENT TYPES
MATHEMATICAL LOGIC
MATHEMATICAL OPERATORS
MATHEMATICS
QUANTUM OPERATORS