2013/03/13 by Eugeniusz Dymek, Dymek, Eugeniusz
Mathematics · Physics and Astronomy · #37B05 #37C29 #37C45 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.1303.3099
openalex publication_date 2013/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For each irrational α∈[0,1) we construct a continuous function f [0,1)→ \R such that the corresponding cylindrical transformation [0,1)×\R \ni (x,t) ↦ (x+α, t+ f(x)) ∈ [0,1)×\R is transitive and the Hausdorff dimension of the set of points whose orbits are discrete is 2. Such cylindrical transformations are shown to display a certain chaotic behaviour of Devaney-like type.