The entropy of a special overlapping dynamical system

Michael Barnsley; Brendan Harding; Andrew Vince

doi:10.1017/etds.2012.140

The entropy of a special overlapping dynamical system

Michael Barnsley, Brendan Harding, Andrew Vince

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

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.

Original language	English
Pages (from-to)	483-500
Number of pages	18
Journal	Ergodic Theory and Dynamical Systems
Volume	34
Issue number	2
DOIs	https://doi.org/10.1017/etds.2012.140
Publication status	Published - Apr 2014

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10.1017/etds.2012.140

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The entropy of a special overlapping dynamical system

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