Seminar in Trieste: Giovanni Panti
Tuesday 4th October at 17:00 (ICTP)
“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.