Ergodic Theory and Dynamical Systems

Table of Contents - 2000 - Volume 20, Issue 05  


An invariant of minimal flows coming from the $K_0$-group of a crossed product $C^*$-algebra

IGOR NIKOLAEV a1
a1 The Fields Institute, 222 College Street, Toronto, M5T 3J1, Canada (e-mail: inikolae@fields.utoronto.ca)

Abstract

Let $M$ be a two-sided surface of genus $g>1$. In 1936 A. Weil singled out the problem of generalization of the Poincarè rotation numbers to the minimal flows $\phi$ on $M$. In this paper we suggest a solution to this problem by constructing the rotation numbers which we call Artin's. These numbers are invariants of the $K_0$-group of a crossed product $C^*$-algebra $C(X)\rtimes_{\phi}\Z$. It is shown that the dynamics of $\phi$ is completely subordinate to diophantine properties of the Artin numbers.

(Received August 10 1998)
(Revised August 26 1999)