Systems of differential equations that are competitive or cooperative. VI: A localCrClosing Lemma for 3-dimensional systems
- 19 September 1991
- journal article
- research article
- Published by Cambridge University Press (CUP) in Ergodic Theory and Dynamical Systems
- Vol. 11 (3) , 443-454
- https://doi.org/10.1017/s014338570000626x
Abstract
For certainCr3-dimensional cooperative or competitive vector fieldsF, whereris any positive integer, it is shown that for any nonwandering pointp, every neighborhood ofFin theCrtopology contains a vector field for whichpis periodic, and which agrees withFoutside a given neighborhood ofp. The proof is based on the existence of invariant planar surfaces throughp.Keywords
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