2022/12/21 by José Pedro Gaivao, Gaivao, José Pedro, Laurent Michel +3 · 1 citation
Computer Science · Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical Dynamics and Fractals #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2212.10944
openalex publication_date 2022/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study maps of the unit interval whose graph is made up of two increasing segments and which are injective in an extended sense. Such maps f\p are parametrized by a quintuple \p of real numbers satisfying inequations. Viewing f\p as a circle map, we show that it has a rotation number ρ(f\p) and we compute ρ(f\p) as a function of \p in terms of Hecke-Mahler series. As a corollary, we prove that ρ(f\p) is a rational number when the components of \p are algebraic numbers.