course: Fuchsian groups, geodesic flows on surfaces of constant negative curvature and symbolic coding of geodesics
speaker: Svetlana Katok (Penn State University)abstract: This will be an introductory course on geodesic flows on surfaces of constant negative curvature and symbolic coding of geodesics. Particular topics will include (parts of) the following: Hyperbolic geometry (geodesics, isometries, hyperbolic area) Fuchsian groups, their fundamental regions, connection with Riemann surfaces Examples: arithmetic Fuchsian groups: modular group and its subgroups; Fuchsian groups derived from quaternion algebras Geodesic flow on a Riemann surface as an example of a dynamical system with complicated "hyperbolic" behavior. Density of closed orbits, topological transitivity and ergodicity with respect to the Liouville measure. Anosov closing lemma and Livshitz theorem for the geodesic flow. Geodesic flow as a special flow over a cross-section. Symbolic coding of geodesics on surfaces of constant negative curvature via a fundamental region. A new approach to coding of geodesics on the modular surface via so-called (a,b)-continued fractions and its relation to Gauss reduction theory
timetable:
Mon 11 Jun, 15:00 - 16:00, Aula Dini
Tue 12 Jun, 15:00 - 16:00, Aula Dini
Wed 13 Jun, 15:00 - 16:00, Aula Dini
Thu 14 Jun, 15:00 - 16:00, Aula Dini
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