Remarks on Joachimsthal Integral and Poritsky Property

Autor:	Serge Tabachnikov, Maxim Arnold
Rok vydání:	2021
Předmět:	Mathematics - Differential Geometry Nonlinear Sciences::Chaotic Dynamics Pure mathematics Mathematics::Dynamical Systems Property (philosophy) Differential Geometry (math.DG) Conic section General Mathematics FOS: Mathematics Dynamical billiards Ellipse Conserved quantity Mathematics
Zdroj:	Arnold Mathematical Journal. 7:483-491
ISSN:	2199-6806 2199-6792
Popis:	The billiard in an ellipse has a conserved quantity, the Joachimsthal integral. We show that the existence of such an integral characterizes conics. We extend this result to the spherical and hyperbolic geometries and to higher dimensions. We connect the existence of Joachimsthal integral with the Poritsky property, a property of billiard curves, called so after H. Poritsky whose important paper Poritsky (Ann Math 51:446–470, 1950) was one of the early studies of the billiard problem.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b4e907bf726027cf7ea6b79a7a8c25bb https://doi.org/10.1007/s40598-021-00180-0 Zobrazit plný text záznamu Full text from SpringerLink