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
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