30 citations · 125 across the 23 of their papers we have counts for
26 papers · 1 filter
Pinched Arnol'd tongues for Families of circle maps
Philip Boyland
We prove that generically for a family of circle maps \begin{equation*} f_{b, ω} (x) = x + ω+ b\, ϕ(x) \end{equation*} with a piecewise linear forcing with breakpoints th…
Dynamical displacements, persistence and semiconjugacies
Philip Boyland
This survey gives a unified treatment of topics from Abelian and non-Abelian Nielsen Theory integrated with the semiconjugacy theorems of Franks and Handel. The main focus is to de…
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…
On the abundance of -fold semi-monotone minimal sets in bimodal circle maps
Philip Boyland
Inspired by a twist maps theorem of Mather we study recurrent invariant sets that are ordered like rigid rotation under the action of the lift of a bimodal circle map to the $k…
Statistical Stability for Barge-Martin attractors derived from tent maps
Philip Boyland, André de Carvalho, Toby Hall
Let be the family of core tent maps of slopes . The parameterized Barge-Martin construction yields a family of disk homeomorphisms ,…