The geodesics for Poincaré's half-plane: a nonstandard derivation

2022/09/22 by Gianluca Gorni, Gorni, Gianluca, Gaetano Zampieri +1
Mathematics · #34C14 #37C79 #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #History and Theory of Mathematics #Homotopy and Cohomology in Algebraic Topology #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2209.10879

openalex publication_date 2022/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Constants of motion are usually derived from groups of symmetry transformation of the system. Here we show that useful properties of the system can be deduced from a family of Noether-like transformations that are not inspired by any symmetry whatsoever. The system here is the Lagrangian interpretation of Poincaré's half plane, and the property is the shape of the geodesics.

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