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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Successional stability of vector fields
in dimension three


Author: Sebastian J. Schreiber
Journal: Proc. Amer. Math. Soc. 127 (1999), 993-1002
MSC (1991): Primary 34D30, 58F12; Secondary 92D40, 92D25
MathSciNet review: 1641101
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Abstract: A topological invariant, the community transition graph, is introduced for dissipative vector fields that preserve the skeleton of the positive orthant. A vector field is defined to be successionally stable if it lies in an open set of vector fields with the same community transition graph. In dimension three, it is shown that vector fields for which the origin is a connected component of the chain recurrent set can be approximated in the $C^1$ Whitney topology by a successionally stable vector field.


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Additional Information

Sebastian J. Schreiber
Affiliation: Department of Mathematics, Western Washington University, Bellingham, Washington 98225
Email: sschreib@cc.wwu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05169-2
PII: S 0002-9939(99)05169-2
Keywords: Generic properties of vector fields, ecological succession, population dynamics
Received by editor(s): January 28, 1997
Additional Notes: Part of this research was completed during a postdoctoral fellowship sponsored by Andrew P. Gutierrez at the University of California, Berkeley. For his support and encouragement, the author is grateful.
Communicated by: Hal L. Smith
Article copyright: © Copyright 1999 American Mathematical Society