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Eigenvalues, $K$-theory and Minimal Flows |
Canad. J. Math. 59(2007), 596-613
Published:2007-06-01
Printed: Jun 2007
Printed: Jun 2007
- Benjamín A. Itzá-Ortiz
Abstract
Let $(Y,T)$ be a minimal suspension flow built over a dynamical
system $(X,S)$ and with (strictly positive, continuous) ceiling
function $f\colon X\to\R$. We show that the eigenvalues of
$(Y,T)$ are contained in the range of a trace on the $K_0$-group
of $(X,S)$. Moreover, a trace gives an order isomorphism of a
subgroup of $K_0(\cprod{C(X)}{S})$ with the group of
eigenvalues of $(Y,T)$. Using this result, we relate the values of
$t$ for which the time-$t$ map on the minimal suspension flow is
minimal with the $K$-theory of the base of this suspension.
| MSC Classifications: |
37A55 - Relations with the theory of $C^*$-algebras [See mainly 46L55] 37B05 - Transformations and group actions with special properties (minimality, distality, proximality, etc.) |