3 papers
math.DS2025
Pinched Arnol'd tongues for Families of circle maps
Philip Boyland
The family of circle maps \begin{equation*} f_{b, Ï} (x) = x + Ï+ b\, Ï(x) \end{equation*} is used as a simple model for a periodically forced oscillator. The parameter rep…
math.DS2025
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 ge…
math.DS2024
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…