2018/09/14 by Pedro L. D. Peres, Peres, Pedro, Ana Rodrigues +1
Computer Science · Mathematics · Physics and Astronomy · #37E20 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Nonlinear Dynamics and Pattern Formation #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.1809.05496
openalex publication_date 2018/09/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we investigate translated cone exchange transformations, a new family of piecewise isometries and renormalize its first return map to a subset of its partition. As a consequence we show that the existence of an embedding of an interval exchange transformation into a map of this family implies the existence of infinitely many bounded invariant sets. We also prove the existence of infinitely many periodic islands, accumulating on the real line, as well as non-ergodicity of our family of maps close to the origin.