5 research outputs found
A characterization of quasi-rational polygons
The aim of this paper is to study quasi-rational polygons related to the
outer billiard. We compare different notions introduced, and make a synthesis
of those.Comment: 15 pages, 9 figure
Outer Billiards outside a Regular Octagon: Periodicity of Almost All Orbits and Existence of an Aperiodic Orbit
Symbolic coding of linear complexity for generic translations of the torus, using continued fractions
In this paper, we prove that almost every translation of admits a symbolic coding which has linear complexity . The partitions are constructed with Rauzy fractals associated with sequences of substitutions, which are produced by a particular extended continued fraction algorithm in projective dimension . More generally, in dimension , we study extended measured continued fraction algorithms, which associate to each direction a subshift generated by substitutions, called -adic subshift. We give some conditions which imply the existence, for almost every direction, of a translation of the torus and a nice generating partition, such that the associated coding is a conjugacy with the subshift