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The entropy of a special overlapping dynamical system

Published online by Cambridge University Press:  30 November 2012

MICHAEL BARNSLEY
Affiliation:
The Australian National University, Canberra, Australia (email: michael.barnsley@anu.edu.au, brendan.harding@anu.edu.au)
BRENDAN HARDING
Affiliation:
The Australian National University, Canberra, Australia (email: michael.barnsley@anu.edu.au, brendan.harding@anu.edu.au)
ANDREW VINCE
Affiliation:
Department of Mathematics, University of Florida, Gainesville, FL, USA (email: avince@ufl.edu)

Abstract

The term special overlapping refers to a certain simple type of piecewise continuous function from the unit interval to itself and also to a simple type of iterated function system (IFS) on the unit interval. A correspondence between these two classes of objects is used (1) to find a necessary and sufficient condition for a fractal transformation from the attractor of one special overlapping IFS to the attractor of another special overlapping IFS to be a homeomorphism and (2) to find a formula for the topological entropy of the dynamical system associated with a special overlapping function.

Type
Research Article
Copyright
©2012 Cambridge University Press 

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