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 explicit models of the natural extension of the maps associated with these algorithms; prove that these natural extensions are...
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 pseudo-Anosov homeomorphism of this type. We also apply a reduction
to finite triangle groups and thereby show the...
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
modular group of its trace field and provide an interval map...