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The Poincare Map in the Regular Neighbourhoods of the Liouville Critical Leaves of an Integrable Hamiltonian System
P. J. Topalov Institute of Mathematics and Informatics,
Acad. G Bonchev Str., bl. 8, t. 113,
Sofia, Bulgaria
Abstract:
In this paper we investigate the Poincare map in the regular neighbourhood of a critical leaf of the Liouville foliation of an integrable Hamiltonian system with two degrees of freedom. It was proved in [3], that for an arbitrary surface transversal to the trajectories, the Poincare map is a one-time-map along the flow of some Hamiltonian, which is defined on the considering surface (this Hamiltonian is called "the Poincare Hamiltonian"). In the paper [4] it was proved that for every transversal surface the Poincare map is a restriction to the surface of some smooth function, which is defined on the regular neighbourhood of the critical leaf.
Received: 05.12.1996
Citation:
P. J. Topalov, “The Poincare Map in the Regular Neighbourhoods of the Liouville Critical Leaves of an Integrable Hamiltonian System”, Regul. Chaotic Dyn., 2:2 (1997), 79–86
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https://www.mathnet.ru/eng/rcd987 https://www.mathnet.ru/eng/rcd/v2/i2/p79
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Abstract page: | 61 |
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