2015/07/09 by Irene Pasquinelli, Pasquinelli, Irene
Engineering · Mathematics · #Adhesion, Friction, and Surface Interactions #Advanced Numerical Analysis Techniques #Dynamical Systems (math.DS) #FOS: Mathematics #Tribology and Lubrication Engineering #math.DS
paper · pdf · doi:10.48550/arxiv.1507.02469
This is the report of the research project done under the supervision of Corinna Ulcigrai at University of Bristol as part of Master 1 programme at Ecole Polytechnique
arxiv created 2015/07/09 · openalex publication_date 2015/07/09 · arxiv updated 2015/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A cutting sequence is a symbolic coding of a linear trajectory on a translation surface corresponding to the sequence of sides hit in a polygonal representation of the surface. We characterize cutting sequences in a regular hexagon with opposite sides identified by translations exploiting the same procedure used by Smillie and Ulcigrai for the regular octagon. In the case of the square, cutting sequences are the well known Sturmian sequences. We remark the differences between the procedure used in the case of the square and the one used in the cases of the regular hexagon and regular octagon. We also show how to adapt the latter to work also in the case of the square, giving a new characterization for this case. We also show how to create a dictionary to pass from the symbolic coding with respect to the hexagon to the symbolic coding with respect to the parallelogram representing it in the space of flat tori. Finally we consider the Bouw-Möller surfaces \mathscr M(3,4) and \mathscr M(4,3) and we use their semi-regular polygons representations to prove our main result, which is a theorem analogous to the central step used to characterize cutting sequences in the previous cases.