17 citations · 93 across the 34 of their papers we have counts for
4 papers · 2 filters
Fractal Homeomorphism for Bi-affine Iterated Function Systems
Michael Barnsley, Andrew Vince
The paper concerns fractal homeomorphism between the attractors of two bi-affine iterated function systems. After a general discussion of bi-affine functions, conditions are provid…
Symmetric Itinerary Sets
Michael F. Barnsley, Nicolae Mihalache
We consider a one parameter family of dynamical systems W :[0, 1] -> [0, 1] constructed from a pair of monotone increasing diffeomorphisms Wsub(i), such that Wsub(i)(inverse): [0,…
Homeomorphisms generated from overlapping affine iterated function systems
Michael F. Barnsley, Brendan Harding, Andrew Vince
We develop the theory of fractal homeomorphisms generated from pairs of overlapping affine iterated function systems.
The Entropy of an Overlapping Dynamical System
Michael F. Barnsley, Brendan Harding, Andrew Vince
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 functio…