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Minimal combinatorial models for maps of an interval with a given set of periods

Published online by Cambridge University Press:  20 June 2003

LOUIS BLOCK ,
ETHAN M. COVEN ,
WILLIAM GELLER  and
KRISTIN HUBNER
LOUIS BLOCK
Affiliation:
Department of Mathematics, University of Florida, Gainesville, FL 32611-8105, USA (e-mail: block@math.ufl.edu)
ETHAN M. COVEN
Affiliation:
Department of Mathematics, Wesleyan University, Middletown, CT 06459-0128, USA
WILLIAM GELLER
Affiliation:
Department of Mathematics, IUPUI, Indianapolis, IN 46202-3216, USA
KRISTIN HUBNER
Affiliation:
Department of Mathematics, Wesleyan University, Middletown, CT 06459-0128, USA Innosoft International Inc., 1050 Lakes Drive, West Covina, CA 91790, USA.
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Abstract

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A combinatorial model for a property of continuous self-maps of a compact interval is a self-map \pi of a finite ordered set such that every continuous \pi-weakly monotone self-map of a compact interval has that property. We identify the minimal combinatorial models for the property ‘the set of periods is a given set’. Here the word minimal refers to the number of points in the domain of the model. We also identify the minimal permutation models and, in appropriate cases, the minimal combinatorial models for properties involving ‘horseshoes’.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 23 , Issue 3 , June 2003 , pp. 707 - 728
Copyright
2003 Cambridge University Press