2021/12/04 by Samuel Everett, Everett, Samuel
Mathematics · Physics and Astronomy · #37C27 (Secondary) #37E99 (Primary) 51N20 #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.2112.02207
openalex publication_date 2021/12/04 · openalex created_date 2021/12/31 · openalex updated_date 2026/07/28
We introduce a geometric dynamical system where iteration is defined as a cycling composition of different maps acting on a space composed of three or more lines in ℝ2. This system is motivated by the dynamics of iterated function systems, as well as billiards with modified reflection laws. We provide conditions under which this dynamical system generates periodic orbits, and use this result to prove the existence of closed nonsmooth curves over ℝ2 which satisfy particular structural constraints with respect to a space of intersecting lines in the plane.