Bounding the number of cycles of O.D.E.s in 𝐑ⁿ

Farkas, M.; van den Driessche, P.; Zeeman, M.

doi:10.1090/S0002-9939-00-05735-X

Bounding the number of cycles of O.D.E.s in ${\mathbf R}^n$
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by M. Farkas, P. van den Driessche and M. L. Zeeman PDF

Proc. Amer. Math. Soc. 129 (2001), 443-449 Request permission

Abstract:

Criteria are given under which the boundary of an oriented surface does not consist entirely of trajectories of the $C^1$ differential equation $\dot {x} = f(x)$ in ${\mathbf R}^n$. 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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