Bouillabaisse Surfaces

Definition

A translation surface is said to be bouillabaisse if it Veech group admits at least two parabolic elements that do not commute. In other terms, the surface can be decomposed into cylinders of commensurable moduli in two different directions.

The name comes from a famous talk given by John Hubbard about Thurston's work on this subject during the conference Dynamique dans l'espace de Teichmüller et applications aux billards rationnels at CIRM in summer 2003.

Some results

• Any Veech surface is a bouillabaisse surface.
• The trace field of such a surface is totally real.

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