Dimension groups for interval maps II: the transitive case

Details Dimension groups for interval maps II: the transitive case Dimension groups for interval maps II: the transitive case

2004-05-24

arxiv.org/abs/math/0405467v2

Mathematics

Dynamical Systems

32 pages, 1 postscript (eps) figure, LateX. minor changes. Has been accepted for publication in Ergodic Theory and Dynamical S

Scientific paper

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.

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