Topology of energy surfaces and existence of transversal Poincare sectionsстатья
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Дата последнего поиска статьи во внешних источниках: 26 сентября 2016 г.
Аннотация:Two questions on the topology of compact energy surfaces of natural two degrees of freedom Hamiltonian systems in a magnetic field are discussed. We show that the topology of this 3-manifold (if it is not a unit tangent bundle) is uniquely determined by the Euler characteristic of the accessible region in configuration space. In this class of 3-manifolds for most cases there does not exist a transverse and complete Poincaré section. We show that there are topological obstacles for its existence such that only in the cases of S^1xS^2 and T^3 such a Poincaré section can exist.