Magic billiards: the case of elliptic boundaries
We introduce a novel concept of magic billiards, which can be viewed as an umbrella unifying several well-known generalisations of mathematical billiards. We analyse the properties of magic billiards in the case of elliptic boundaries. We provide explicit conditions for periodicity in algebro-geometric, analytic and polynomial forms. A topological description of these billiards is given using Fomenko graphs. Bibliography: 45 titles.
Authors
- Vladimir Dragović (ORCID: https://orcid.org/0000-0002-0295-4743)
- Milena Radnović (ORCID: https://orcid.org/0000-0002-7728-8036)
Institutions
- The University of Sydney (AU)
- Serbian Academy of Sciences and Arts (RS)
- The University of Texas at Dallas (US)
- UNSW Sydney (AU)
Publication Details
- Journal
- Sbornik Mathematics
- Published
- 2025-01-01
- DOI
- https://doi.org/10.4213/sm10181e
- Primary Topic
- Mathematical Dynamics and Fractals
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Simons Foundation
- University of New South Wales
- Ministarstvo Prosvete, Nauke i Tehnološkog Razvoja
- Serbian Academy of Sciences and Arts
- Australian Research Council