Topology of energy surfaces and existence of transversal Poincaré sections

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dc.creatorBolsinov, Alexey
dc.creatorDullin, Holger R.
dc.creatorWittek, Andreas
dc.date1996-02-29
dc.date.accessioned2026-07-07T09:07:54Z
dc.date.available2026-07-07T09:07:54Z
dc.descriptionTwo 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 $S^1\times S^2$ and $T^3$ such a Poincaré section can exist.
dc.description10 pages, LaTex
dc.identifierhttps://arxiv.org/abs/chao-dyn/9602023
dc.identifierhttp://arxiv.org/abs/chao-dyn/9602023
dc.identifierJ. Phys. A, 29:4977--4985, 1996
dc.identifierdoi:10.1088/0305-4470/29/16/019
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/150531
dc.subjectChaotic Dynamics
dc.titleTopology of energy surfaces and existence of transversal Poincaré sections
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