Memoirs of the American Mathematical Society 2011; 53 pp; softcover Volume: 209 ISBN10: 0821853023 ISBN13: 9780821853023 List Price: US$60 Individual Members: US$36 Institutional Members: US$48 Order Code: MEMO/209/982
 Let \(X\) be a locally compact Hausdorff space with \(n\) proper continuous self maps \(\sigma_i:X \to X\) for \(1 \le i \le n\). To this the authors associate two conjugacy operator algebras which emerge as the natural candidates for the universal algebra of the system, the tensor algebra \(\mathcal{A}(X,\tau)\) and the semicrossed product \(\mathrm{C}_0(X)\times_\tau\mathbb{F}_n^+\). They develop the necessary dilation theory for both models. In particular, they exhibit an explicit family of boundary representations which determine the C*envelope of the tensor algebra. Table of Contents  Introduction
 Dilation theory
 Recovering the dynamics
 Semisimplicity
 Open problems and future directions
 Bibliography
