Veech Surfaces with Non-periodic Directions in the Trace Field
نویسندگان
چکیده
Veech’s original examples of translation surfaces Vq enjoying what McMullen has dubbed “optimal dynamics” arise from appropriately gluing sides of two copies of the regular qgon, with q ≥ 3 . We show that every Vq whose trace field is of degree greater than 2 has non-periodic directions of vanishing SAF-invariant. (Calta-Smillie have shown that under appropriate normalization, the set of slopes of directions where this invariant vanishes agrees with the trace field.) Furthermore, we give explicit examples of pseudo-Anosov diffeomorphisms whose contracting direction has zero SAF-invariant. In an appendix, we prove various elementary results on the containment of trigonometric fields.
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