Joshua P. Bowman

activity

20102021

most citedThe complete family of Arnoux-Yoccoz surfaces

1 citations · 1 across the 1 of their papers we have counts for

collaborators

4 papers

math.DS2021

Iterated monodromy groups of Chebyshev-like maps on $C^{n}$

Joshua P. Bowman

Every affine Weyl group appears as the iterated monodromy group of a Chebyshev-like polynomial self-map of $C^{n}$ .

math.GT2020

Geometry and Algebra of the Deltoid Map

Joshua P. Bowman

The geometry of the deltoid curve gives rise to a self-map of $C^{2}$ that is expressed in coordinates by $f (x, y) = (y^{2} - 2 x, x^{2} - 2 y)$ . This is one in a family of maps th…

math.GT2018

Angels' staircases, Sturmian sequences, and trajectories on homothety surfaces

Joshua Bowman, Slade Sanderson

A homothety surface can be assembled from polygons by identifying their edges in pairs via homotheties, which are compositions of translation and scaling. We consider linear trajec…

math.GT2010★ 1 cited

The complete family of Arnoux-Yoccoz surfaces

Joshua P. Bowman

The family of translation surfaces $(X_{g}, ω_{g})$ constructed by Arnoux and Yoccoz from self-similar interval exchange maps encompasses one example from each genus $g$ greater than or…

Iterated monodromy groups of Chebyshev-like maps on Cn

Geometry and Algebra of the Deltoid Map

Angels' staircases, Sturmian sequences, and trajectories on homothety surfaces

The complete family of Arnoux-Yoccoz surfaces

Iterated monodromy groups of Chebyshev-like maps on $C^{n}$