Eigenvalues, K-theory and Minimal Flows

Abstract

Let $(Y,T)$ be a minimal suspension flow built over a dynamical system $(X,S)$ and with (strictly positive, continuous) ceiling function $f:X\to \mathbb{R}$. 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 $K_0(C(X){⋊}_S\mathbb{Z})$ with the group of eigenvalues of $(Y,S)$. Using this result, we relate the values of $t$ for which the time-$t$ map on minimal suspension flow is minimal, with the $K$-theory of the base of this suspension.

arXiv comment19 pages