ICTP Mathematics Seminar - Tuesday, 4 October at 17:00

[Math Group]

M A T H E M A T I C S   S E M I N A R S  2016


Tuesday, 4 October, at 17.00 hrs.


Giovanni Panti (University of Udine)


Title: A geometric model for the natural extension of continued fraction 
maps


Abstract:
Just as classical "Floor" continued fractions induce the Gauss map on 
the real unit interval, other euclidean division algorithms (Ceiling, 
Even, Odd, NearestInteger, ...) induce piecewise-fractional maps with 
integer coefficients. All these maps have natural extensions that can 
easily be described on an ad hoc basis. We present a general framework 
for dealing with all these maps in a uniform way. The construction is 
geometric and well visualizable, exploiting both the interpretation of 
continued fractions as symbolic dynamics for the geodesic flow on the 
modular surface, and the projective duality between the hyperbolic plane 
and the de Sitter space.


VENUE: Luigi Stasi Seminar Room (ICTP Leonardo da Vinci Building, first 
floor)