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

Abstract

For certainC^r3-dimensional cooperative or competitive vector fieldsF, whereris any positive integer, it is shown that for any nonwandering pointp, every neighborhood ofFin theC^rtopology 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.