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Infinite sequence of fixed point free pseudo-Anosov homeomorphisms on a family of genus two surfaces. (English) Zbl 1217.37040
Kolyada, Sergiy (ed.) et al., Dynamical numbers. Interplay between dynamical systems and number theory. A special program, May 1–July 31, 2009. International conference, MPI, Bonn, Germany, July 20–24, 2009. Proceedings. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4958-3). Contemporary Mathematics 532, 231-242 (2010).
Summary: We construct an infinite sequence of pseudo-Anosov homeomorphisms without fixed separatrix, and leaving invariant a family of genus two translation surfaces with a single zero. This extends previous work of J. Los [Ergodic Theory Dyn. Syst. 30, No. 6, 1739–1755 (2010; Zbl 1213.37071)]. The construction uses the Rauzy-Veech induction.
For the entire collection see [Zbl 1205.00087].

37E05 Dynamical systems involving maps of the interval (piecewise continuous, continuous, smooth)
37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)