First expansive returns and cross sections

Tom Schmidt (Oregon State U, Corvallis)

Apr 24. 2025, 11:30 — 12:00

With Calta and Kraaikamp we studied alpha-type families of continued fraction-like interval maps for each of a countably infinite collection of Fuchsian triangle groups.   We showed that the measure theoretic entropy defines a continuous function of the parameter for each family.   We introduced a notion of `first expansive power' of an interval map and conjectured that  the first expansive power for each of our maps defines a system  whose natural extension is given by a cross section to the geodesic flow on the unit tangent bundle of the hyperbolic surface uniformized by the corresponding triangle group.   I will present a proof of the conjecture, after sketching background and motivation.

Further Information
Venue:
ESI Boltzmann Lecture Hall
Recordings:
Recording
Associated Event:
Uniform Distribution of Sequences (Workshop)
Organizer(s):
Henk Bruin (U of Vienna)
Robbert Fokkink (TU Delft)
Jörg Thuswaldner (Montanuniversität Leoben)