The Classification Theorem for Liouville Torus Surgery

Some of the above-said types of surgery have already been discovered in concrete important mechanical systems. See the papers by Kharlamov and Pogosyan [177] and [185]. For instance, this is the surgery on tori in the case of Kovalevskaya 

As in the four-dimensional case, one could distinguish between orientable and nonorientable Hamiltonians H, We call a Hamiltonian orientable if all of its critical submanifolds (on are orientable, that is, there is not a single critical manifold 

Proposition 2.2.1. If U(X ) sgradfT /2,---,/n) integrable Hamiltonian system with a Bott nonorientable Hamiltonian H on a surface then it may always be doubly covered by a Hamiltonian system 

Let t be an integrable system on Af. Fix the values of all last integrals f2i - fn and suppose that the obtained (n + l)-dimensional surface is com- 

Kozlov has noted to the author that it b of importance that limit degeneracies actually arise in concrete mechanical systems with dissipation. 

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