Eigenvalues, $K$ -theory and Minimal Flows

Itzá-Ortiz, Benjamín A.

Canadian journal of mathematics, Tome 59 (2007) no. 3, pp. 596-613

Résumé

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 ${{K}_{0}}\left( C(X)\,{{\rtimes }_{S}}\,\mathbb{Z} \right)$ 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.

Détail

DOI : 10.4153/CJM-2007-025-5

Mots-clés : 37A55, 37B05

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