Authors: Gasiorek, Sean
Radnović, Milena
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Pseudo-Euclidean billiards within confocal curves on the hyperboloid of one sheet
Journal: Journal of Geometry and Physics
Volume: 161
First page: 104032
Issue Date: 2021
Rank: M21
ISSN: 0393-0440
DOI: 10.1016/j.geomphys.2020.104032
Abstract: 
We consider a billiard problem for compact domains bounded by confocal conics on a hyperboloid of one sheet in the Minkowski space. We show that there are two types of confocal families in such setting. Using an algebro-geometric integration technique, we prove that the billiard within generalized ellipses of each type is integrable in the sense of Liouville. Further, we prove a generalization of the Poncelet theorem and derive Cayley-type conditions for periodic trajectories and explore geometric consequences.
Keywords: Billiards | Confocal quadrics | Elliptic billiards | Geodesics | Minkowski space | Periodic trajectories; Mathematics - Dynamical Systems; Mathematics - Dynamical Systems; 70H06, 70H12, 37J35, 37J46 (Primary) 14H70, 37J38, 37J39 (Secondary)
Publisher: Elsevier

Show full item record

SCOPUSTM   
Citations

3
checked on Dec 26, 2024

Page view(s)

22
checked on Dec 26, 2024

Google ScholarTM

Check

Altmetric

Altmetric


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.