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

Date: 2001-01-01

Creator: M. Farkas, P. Van Den Driessche, M. L. Zeeman

Access: Open access

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. ©2000 American Mathematical Society.