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Smooth invariants of focus-focus singularities

A. M. Izosimov

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: 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 has been constructed, which makes it possible to classify focus–focus singularities up to a $\mathrm{C}^1$-diffeomorphism.

Key words: Hamiltonian systems, singularities, integrability.

UDC: 517.938.5

Received: 24.12.2010

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