Angle contraction between geodesics

2009/02/02 by Nikolai A. Krylov, Krylov, Nikolai A., Edwin L. Rogers +1
Engineering · Mathematics · #40A05 #53A05 #Advanced Numerical Analysis Techniques #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #Dynamics and Control of Mechanical Systems #FOS: Mathematics #math.DG #math.DS #msc:40A05 #msc:53A05

paper · pdf · doi:10.48550/arxiv.0902.0315

10 pages, 2 figures

arxiv created 2009/02/02 · openalex publication_date 2009/02/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider here a generalization of a well known discrete dynamical system produced by the bisection of reflection angles that are constructed recursively between two lines in the Euclidean plane. It is shown that similar properties of such systems are observed when the plane is replaced by a regular surface in \mathbb R³ and lines are replaced by geodesics. An application of our results to the classification of points on the surface as elliptic, hyperbolic or parabolic is also presented.

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