Bifurcation diagram and the discriminant of a spectral curve of integrable systems on Lie algebras

Journal Article · Thu Nov 11 00:00:00 EST 2010 · Sbornik. Mathematics

DOI:https://doi.org/10.1070/SM2010V201N09ABEH004112· OSTI ID:21418066

Konyaev, Andrei Yu ^[1]

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

A bifurcation diagram is a stratified (in general, nonclosed) set and is one of the efficient tools of studying the topology of the Liouville foliation. In the framework of the present paper, the coincidence of the closure of a bifurcation diagram {Sigma}-bar of the moment map defined by functions obtained by the method of argument shift with the closure of the discriminant D-bar{sub z} of a spectral curve is proved for the Lie algebras sl(n+1), sp(2n), so(2n+1), and g{sub 2}. Moreover, it is proved that these sets are distinct for the Lie algebra so(2n). Bibliography: 22 titles.

• OSTI ID: 21418066
• Journal Information: Sbornik. Mathematics, Vol. 201, Issue 9; Other Information: DOI: 10.1070/SM2010v201n09ABEH004112; ISSN 1064-5616
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
BIBLIOGRAPHIES
BIFURCATION
FUNCTIONS
INTEGRAL CALCULUS
LIE GROUPS
MAPS
TOPOLOGY
DOCUMENT TYPES
MATHEMATICS
SYMMETRY GROUPS