A counterexample to a multidimensional version of the weakened Hilbert's 16-th problem

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dc.creatorBobienski, Marcin
dc.creatorZoladek, Henryk
dc.date2006-02-06
dc.date.accessioned2026-07-07T07:03:09Z
dc.date.available2026-07-07T07:03:09Z
dc.descriptionIn the weakened 16th Hilbert's Problem one asks for a bound of the number of limit cycles which appear after a polynomial perturbation of a planar polynomial Hamiltonian vector field. It is known that this number is finite for an individual vector field. In the multidimensional generalization of this problem one considers polynomial perturbation of a polynomial vector field with invariant plane supporting a Hamiltonian dynamics. We present an explicit example of such perturbation with infinite number of limit cycles which accumulate at some separatrix loop.
dc.description17 pages, 3 figures
dc.identifierhttps://arxiv.org/abs/math/0602099
dc.identifierhttp://arxiv.org/abs/math/0602099
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/108862
dc.subjectDynamical Systems
dc.subject34C07, 34C08
dc.titleA counterexample to a multidimensional version of the weakened Hilbert's 16-th problem
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