Toby Hall

activity

20022023

most citedNew Rotation Sets in a Family of Torus Homeomorphisms

30 citations · 124 across the 17 of their papers we have counts for

collaborators

21 papers

math.DS2023

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…

math.DS2023

Unimodal Measurable Pseudo-Anosov Maps

Philip Boyland, André de Carvalho, Toby Hall

We exhibit a continuously varying family $F_{λ}$ of homeomorphisms of the sphere $S^{2}$ , for which each $F_{λ}$ is a measurable pseudo-Anosov map. Measurable pseudo-Anosov maps are gene…

math.GT2019

Limits of sequences of pseudo-Anosov maps and of hyperbolic 3-manifolds

Sylvain Bonnot, André de Carvalho, Juan González-Meneses +1

There are two objects naturally associated with a braid $β \in B_{n}$ of pseudo-Anosov type: a (relative) pseudo-Anosov homeomorphism $φ_{β} : S^{2} \to S^{2}$ ; and the finite volume com…

math.DS2018

Statistical Stability for Barge-Martin attractors derived from tent maps

Philip Boyland, André de Carvalho, Toby Hall

Let ${f_{t}}_{t \in (1, 2]}$ be the family of core tent maps of slopes $t$ . The parameterized Barge-Martin construction yields a family of disk homeomorphisms $Φ_{t} : D^{2} \to D^{2}$ ,…

math.GT2017

Intersections of multicurves from Dynnikov coordinates

S. Öykü Yurttas, Toby Hall

We present an algorithm for calculating the geometric intersection number of two multicurves on the $n$ -punctured disk, taking as input their Dynnikov coordinates. The algorithm ha…

math.DS2017

Typical path components in tent map inverse limits

Philip Boyland, André de Carvalho, Toby Hall

In the inverse limit $I^_{s}$ of a tent map $f_{s}$ restricted to its core, the set $G R$ of points whose path components are bi-infinite and bi-dense has full measure…