Ergodic Theory and Dynamical Systems

Research Article

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

Morris W. Hirscha1

a1 Department of Mathematics, University of California Berkeley, CA 94720, USA

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.

(Received August 23 1989)