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

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16 papers · 1 filter

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.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.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…

math.DS2017★ 8 cited

Natural extensions of unimodal maps: virtual sphere homeomorphisms and prime ends of basin boundaries

Philip Boyland, André de Carvalho, Toby Hall

Let ${f_{t} : I \to I}$ be a family of unimodal maps with topological entropies $h (f_{t}) > \frac{1}{2} lo g 2$ , and $f_{t} : I_{t} \to I_{t}$ be their nat…

math.DS2017★ 7 cited

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 ${0, 1}^{Z}$ to be the itinerary of a point of the inverse limit of a tent map are expressed in terms of f…