 
Summary: manuscripta math. 72, 415  423 (1991) manuscripta
mathematica
9 SpringerVerlag 1991
COHOMOLOGY AND ASYMPTOTIC STABILITY OF
CONTINUA
Konstantin Athanassopoulos
IDIMENSIONAL
We prove that a ldimensional continuum carrying a flow without
singular points is homeomorphic to the unit circle if its first Cech
cohomology group with integer coefficients is isomorphic to Z . As
an application of this we obtain that an asymptotically stable inva
riant ldimensional continuum of a flow on a locally compact ANR,
which does not contain singular points, must be a periodic orbit.
I. Introduction
Two of the most interesting problems in the theory of dynamical
systems are to determine the structure of the limit sets and describe
the behavior of the orbits near them. A serious step in this direction
is the study of minimal sets, since every compact limit set contains
a minimal set.
The original motivation of this note is the problem of finding
