Arnoux, Pierre; Schmidt, Thomas A.(American Institute of Mathematical Sciences, 2014-11)

We compare two families of continued fractions algorithms, the
symmetrized Rosen algorithm and the Veech algorithm. Each of these algorithms
expands real numbers in terms of certain algebraic integers. We give
explici ...

Calta, Kariane; Schmidt, Thomas A.(Australian Mathematical Publishing Association Inc., 2013-02-07)

We give continued fraction algorithms for each conjugacy class of triangle Fuchsian group of signature
(3, n, ∞), with n ≥ 4. In particular, we give an explicit form of the group that is a subgroup of the Hilbert
modu ...

Calta, Kariane; Schmidt, Thomas A.(American Institute of Mathematical Sciences, 2013-06)

We give explicit pseudo-Anosov homeomorphisms with vanishing
Sah–Arnoux–Fathi invariant. Any translation surface whose Veech group
is commensurable to any of a large class of triangle groups is shown to have
an affine ...