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Bounding the Number of Cycles of O.D.E.S in Rn

M. Farkas, P. Van Den Driessche and M. L. Zeeman
Proceedings of the American Mathematical Society
Vol. 129, No. 2 (Feb., 2001), pp. 443-449
Stable URL: http://www.jstor.org/stable/2668703
Page Count: 7
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Bounding the Number of Cycles of O.D.E.S in Rn
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Abstract

Criteria are given under which the boundary of an oriented surface does not consist entirely of trajectories of the C1 differential equation ẋ = f(x) in Rn. The special case of an annulus is further considered, and the criteria are used to deduce sufficient conditions for the differential equation to have at most one cycle. A bound on the number of cycles on surfaces of higher connectivity is given by similar conditions.

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