17 citations · 64 across the 22 of their papers we have counts for
5 papers · 1 filter
Fractal Continuation
Michael F. Barnsley, Andrew Vince
A fractal function is a function whose graph is the attractor of an iterated function system. This paper generalizes analytic continuation of an analytic function to continuation o…
A Combinatorial Approach to Positional Number Systems
Andrew Vince
Although the representation of the real numbers in terms of a base and a set of digits has a long history, new questions arise even in simple situations. This paper concerns binary…
A Combinatorial Characterization of the Critical Itineraries of a Uniform Dynamical System
Michael Barnsley, Wolfgang Steiner, Andrew Vince
For a function from the unit interval to itself with constant slope and one discontinuity, the itineraries of the point of discontinuity are called the critical itineraries. These…
Embedding the symbolic dynamics of Lorenz maps
Tony Samuel, Nina Snigireva, Andrew Vince
Necessary and sufficient conditions for the symbolic dynamics of a Lorenz map to be fully embedded in the symbolic dynamics of a piecewise continuous interval map are given. As an…
The Number of Ways to Assemble a Graph
Andrew Vince, Miklos Bona
Motivated by the question of how macromolecules assemble, the notion of an {\it assembly tree} of a graph is introduced. Given a graph , the paper is concerned with enumerating…