The Entropy of an Overlapping Dynamical System
Dynamical Systems
2015-03-19 v2
Abstract
The term "overlapping" refers to a certain fairly simple type of piecewise continuous function from the unit interval to itself and also to a fairly 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 overlapping IFS to the attractor of another overlapping IFS to be a homeomorphism and (2) to find a formula for the topological entropy of the dynamical system associated with an overlapping function.
Cite
@article{arxiv.1110.6692,
title = {The Entropy of an Overlapping Dynamical System},
author = {Michael F. Barnsley and Brendan Harding and Andrew Vince},
journal= {arXiv preprint arXiv:1110.6692},
year = {2015}
}
Comments
Includes correction to Lemma 6.2