Smooth invariants of focus-focus singularities

Smooth invariants of focus-focus singularities

We consider focus-focus singularities of integrable Hamiltonian systems with two degrees of freedom. It is known that if two singularities of this kind have the same number of singular points, then they are fiber-wise homeomorphic. However, it may happen that this homeomorphism cannot be made smooth...

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Veröffentlicht in:Moscow University mathematics bulletin 2011-08, Vol.66 (4), p.178-180
1. Verfasser: Izosimov, A. M.
Format: Artikel
Sprache:eng
Schlagworte:
Analysis
Brief Communications
Mathematics
Mathematics and Statistics
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Zusammenfassung:We consider focus-focus singularities of integrable Hamiltonian systems with two degrees of freedom. It is known that if two singularities of this kind have the same number of singular points, then they are fiber-wise homeomorphic. However, it may happen that this homeomorphism cannot be made smooth. An invariant is constructed, which makes it possible to classify focus-focus singularities up to a C 1 -diffeomorphism.
ISSN:0027-1322
1934-8444
DOI:10.3103/S0027132211040103