 
Summary: Math. Proc. Camb. Phil. Soc. (1999), 127, 83
Printed in the United Kingdom c 1999 Cambridge Philosophical Society
83
Chain recurrence in flows on the Klein bottle
By ATHANASSIOS ALEXELLIS
Aetorachis 4243, GR11146 Galatsi, Athens, Greece
and KONSTANTIN ATHANASSOPOULOS
Department of Mathematics, University of Crete, GR71409 Iraklion, Greece
(Received 14 April 1998)
1. Introduction
In the classical PoincarŽeBendixson theory the object of study are the limit sets
of a continuous flow on the 2sphere S2
and the behaviour of the orbits near them
(see [7, 9]). In [2] the second author proved that an assertion similar to the PoincarŽe
Bendixson theorem is true in the wider class of the 1dimensional invariant (inter
nally) chain recurrent continua of flows on S2
. On the other hand, it is known that
among the closed 2manifolds, the 2sphere S2
, the projective plane RP2
and the
