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Dimension groups for interval maps II: the transitive case

Published online by Cambridge University Press:  22 June 2007

FRED SHULTZ
FRED SHULTZ
Affiliation:
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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 27 , Issue 4 , August 2007 , pp. 1287 - 1321
Copyright
2007 Cambridge University Press

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