Summary: manuscripta math. 72, 415 - 423 (1991) manuscripta
9 Springer-Verlag 1991
COHOMOLOGY AND ASYMPTOTIC STABILITY OF
We prove that a l-dimensional 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 l-dimensional continuum of a flow on a locally compact ANR,
which does not contain singular points, must be a periodic orbit.
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