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- Title
Dimension groups for interval maps II: the transitive case.
- Authors
FRED SHULTZ
- 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.
- Subjects
TOPOLOGICAL dynamics; TOPOLOGICAL entropy; DIFFERENTIABLE dynamical systems; SYSTEMS theory; MATHEMATICAL mappings
- Publication
Ergodic Theory & Dynamical Systems, 2007, Vol 27, Issue 4, p1287
- ISSN
0143-3857
- Publication type
Article
- DOI
10.1017/S014338570700003X