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This article is cited in 5 scientific papers (total in 5 papers)
A counterexample to a multidimensional version of the weakened Hilbert's 16th problem
M. Bobieński, H. Żołądek Institute of Mathematics, Warsaw University
Abstract:
In the weakened 16th Hilbert's Problem one asks for a bound on 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 an invariant plane supporting a Hamiltonian dynamics. We present an explicit example of such perturbation with an infinite number of limit cycles which accumulate at some separatrix loop.
Key words and phrases:
Polynomial vector field, limit cycle, invariant manifold, Abelian integral.
Received: January 19, 2006; in revised form June 7, 2006
Citation:
M. Bobieński, H. Żołądek, “A counterexample to a multidimensional version of the weakened Hilbert's 16th problem”, Mosc. Math. J., 7:1 (2007), 1–20
Linking options:
https://www.mathnet.ru/eng/mmj268 https://www.mathnet.ru/eng/mmj/v7/i1/p1
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Abstract page: | 287 | Full-text PDF : | 2 | References: | 73 |
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