 
Summary: Math. Z. 223, 643649 (1996)
Mathematische
ZeitschriftSpringerVerlag 1996
Onedimensional chain recurrent sets of flows
in the 2sphere
K. Athanassopoulos
Departmentof Mathematics,Universityof Crete, GR71409Iraklion,Greece
email: athanako@talos.cc.uch.gr
Received 19 September 1994;in finalform27 February 1995
1. Introduction
The subject of the classical PoincareBendixson theory is the study of the struc
ture of the limit sets of flows in the 2sphere S 2 and the behavior of the orbits
near them. A fairly complete account of the theory is given in [3]. A limit set
of a flow in S 2 which contains at least one nonsingular point is 1dimensional,
compact, connected, invariant and the restricted flow on it is chain recurrent. The
motivation of this note was to examine what properties of limit sets can be ex
tended to the class of 1dimensional invariant chain recurrent continua for flows
in S 2. It seems that some basic properties do extend. For instance, an assertion
similar to the PoincareBendixson theorem is true in this wider class. Precisely,
if a 1dimensional invariant chain recurrent continuum of a flow in S 2 contains
