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Systems of differential equations that are competitive or cooperative. VI: A local Cr Closing Lemma for 3-dimensional systems

Published online by Cambridge University Press:  19 September 2008

Morris W. Hirsch
Morris W. Hirsch
Affiliation:
Department of Mathematics, University of California Berkeley, CA 94720, USA
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Abstract

For certain Cr 3-dimensional cooperative or competitive vector fields F, where r is any positive integer, it is shown that for any nonwandering point p, every neighborhood of F in the Cr topology contains a vector field for which p is periodic, and which agrees with F outside a given neighborhood of p. The proof is based on the existence of invariant planar surfaces through p.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 11 , Issue 3 , September 1991 , pp. 443 - 454
Copyright
Copyright © Cambridge University Press 1991

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