2021/06/29 by Yury Kochetkov, Kochetkov, Yury
Mathematics · #Advanced Differential Equations and Dynamical Systems #Combinatorics #Computer science #FOS: Mathematics #Geology #Geometry #Mathematical Dynamics and Fractals #Mathematics #Metric Geometry (math.MG) #Midpoint #Plane (geometry) #Point processes and geometric inequalities #Quadrangle #Regular polygon #Space (punctuation) #math.MG
paper · pdf · doi:10.48550/arxiv.2106.15557
published in arXiv (Cornell University) (Cornell University) · 4 pages, 4 figures
arxiv created 2021/06/29 · openalex publication_date 2021/06/29 · arxiv updated 2021/06/30 · openalex created_date 2021/07/05 · openalex updated_date 2026/07/28
Let us consider a family F(α,β,γ,δ) of convex quadrangles in the plane with given angles \α,β,γ,δ\ and with the perimeter 2π. Such quadrangle Q∈ F(α,β,γ,δ) can be considered as a point (x1,x2,x3,x4)∈ℝ4, where \x1,x2,x3,x4\ are lengths of edges. Then to F a finite open segment I⊂ℝ4 is corresponded. A quadrangle in F, that corresponds to the midpoint of I is called a balanced quadrangle. Let M be the set of balanced quadrangles. The function f:M→ M is defined in the following way: angles of the balanced quadrangle Q', Q'=f(Q), are numerically equal to edges of Q. The map f defines a dynamical system in the space of balanced quadrangles. In this work we study properties of this system.