Ergodic Theory and Dynamical Systems

Table of Contents - 2007 - Volume 27, Issue 04  


Dimension groups for interval maps II: the transitive case

FRED SHULTZ a1
a1 Wellesley College, Wellesley, MA 02481, USA (e-mail: fshultz@wellesley.edu)

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Abstract

Any continuous, transitive, piecewise monotonic map is determined up to a binary choice by its dimension module with the associated finite sequence of generators. The dimension module by itself determines the topological entropy of any transitive piecewise monotonic map, and determines any transitive unimodal map up to conjugacy. For a transitive piecewise monotonic map which is not essentially injective, the associated dimension group is a direct sum of simple dimension groups, each with a unique state.

(Published Online June 22 2007)
(Received June 28 2004)
(Revised June 5 2005)