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Dynamics Seminar
April 23, 2008

Ilie Ugarcovici
DePaul University

Geodesic flows, cross-section maps and generalized continued fractions

We construct a two-parameter family of continued fractions and derive some dynamical properties based on connections with the geodesic flow on the modular surface. We show how natural extension maps can be realized geometrically as cross-section maps of the geodesic flow. Some possible generalizations of Bowen-Series boundary maps associated to arbitrary Fuchsian groups will be also described. This is joint work with S. Katok and D. Zagier.

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