30 citations · 66 across the 13 of their papers we have counts for
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The Dynamics of Measurable Pseudo-Anosov Maps
Philip Boyland, André de Carvalho, Toby Hall
We study the dynamics of measurable pseudo-Anosov homeomorphisms of surfaces, a generalization of Thurston's pseudo-Anosov homeomorphisms. A measurable pseudo-Anosov map has a tran…
Unimodal Measurable Pseudo-Anosov Maps
Philip Boyland, André de Carvalho, Toby Hall
We exhibit a continuously varying family of homeomorphisms of the sphere , for which each is a measurable pseudo-Anosov map. Measurable pseudo-Anosov maps are gene…
Itineraries for Inverse Limits of Tent Maps: a Backward View
Philip Boyland, André de Carvalho, Toby Hall
Previously published admissibility conditions for an element of to be the itinerary of a point of the inverse limit of a tent map are expressed in terms of f…
Julia sets for Fibonacci endomorphisms of and
S. Bonnot, A. de Carvalho, A. Messaoudi
We study the dynamics of the family of endomorphisms of and , where is a real or complex parameter. Such maps can be seen as…
New Rotation Sets in a Family of Torus Homeomorphisms
Philip Boyland, André de Carvalho, Toby Hall
We construct a family of homeomorphisms of the two-torus isotopic to the identity, for which all of the rotation sets can be described explicitly. We…
On digit frequencies in β-expansions
Philip Boyland, André de Carvalho, Toby Hall
We study the sets DF(β) of digit frequencies of β-expansions of numbers in [0,1]. We show that DF(β) is a compact convex set with countably many extreme points which varies continu…