Veech surfaces with non-periodic directions in the trace field

2009/06/24 by Pierre Arnoux, Thomas Schmidt, Arnoux, Pierre +1
Mathematics · Physics and Astronomy · #11J70 #30F60 #37D99 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.0906.4571

openalex publication_date 2009/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that each of Veech's original examples of translation surfaces with ``optimal dynamics'' whose trace field is of degree greater than two has non-periodic directions of vanishing SAF-invariant. Furthermore, we give explicit examples of pseudo-Anosov diffeomorphisms whose contracting direction has zero SAF-invariant.

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