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

Authors:
M. Farkas, P. van den Driessche and M. L. Zeeman

Journal:
Proc. Amer. Math. Soc. **129** (2001), 443-449

MSC (2000):
Primary 34A26, 34C05, 34C25, 37C27

Published electronically:
July 27, 2000

MathSciNet review:
1800234

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Abstract | References | Similar Articles | Additional Information

Criteria are given under which the boundary of an oriented surface does not consist entirely of trajectories of the 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.

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Additional Information

**M. Farkas**

Affiliation:
School of Mathematics, University of Technology, H-1521 Budapest, Hungary

Email:
fm@math.bme.hu

**P. van den Driessche**

Affiliation:
Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada V8W 3P4

Email:
pvdd@smart.math.uvic.ca

**M. L. Zeeman**

Affiliation:
Division of Mathematics and Statistics, University of Texas at San Antonio, San Antonio, Texas 78249-0664

Email:
zeeman@math.utsa.edu

DOI:
https://doi.org/10.1090/S0002-9939-00-05735-X

Keywords:
Bendixson-Dulac,
cycles,
periodic orbit,
genus,
Stokes' Theorem

Received by editor(s):
April 18, 1999

Published electronically:
July 27, 2000

Additional Notes:
The first author’s research was supported in part by the Hungarian Foundation for Scientific Research grant no. T029893

The second author’s research was supported in part by an NSERC Research Grant and the University of Victoria Committee on Faculty Research and Travel.

The third author’s research was supported in part by the University of Texas at San Antonio Office of Research Development.

Communicated by:
Hal L. Smith

Article copyright:
© Copyright 2000
American Mathematical Society