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Bounding the number of cycles of O.D.E.s in |
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| Authors: | M Farkas P van den Driessche M L Zeeman |
| Institution: | School of Mathematics, University of Technology, H-1521 Budapest, Hungary ; Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada V8W 3P4 ; Division of Mathematics and Statistics, University of Texas at San Antonio, San Antonio, Texas 78249-0664 |
| Abstract: | Criteria are given under which the boundary of an oriented surface does not consist entirely of trajectories of the |
| Keywords: | Bendixson-Dulac cycles periodic orbit genus Stokes' Theorem |
| 点击此处可从《Proceedings of the American Mathematical Society》浏览原始摘要信息 | |
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differential equation 
in 
. 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.