2020/10/05 by Ferenczi, Sébastien, Hubert, Pasacal
Computer Science · Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Mathematics and Applications #Primary 37E05 #Secondary 37B10 #semigroups and automata theory
paper · doi:10.48550/arxiv.2010.01860
openalex publication_date 2020/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We look at d-point extensions of a rotation of angle α with r marked points, generalizing the examples of Veech 1969 and Sataev 1975, together with the square-tiled interval exchange transformations of \citefh2. We study the property of rigidity, in function of the Ostrowski expansions of the marked points by α: we prove that T is rigid when α has unbounded partial quotients, and that T is not rigid when the natural coding of the underlying rotation with marked points is linearly recurrent. But there remains an interesting grey zone between these two cases, in which we have only partial results on the rigidity question; they allow us to build the first examples of non linearly recurrent and non rigid interval exchange transformations.