This analysis details periodicity conditions in magic billiards with elliptic boundaries, highlighting topological aspects.
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.
No takes yet. Share an insight, caveat, or question.
Dragović et al. (2025) studied this question.
Synapse has enriched one closely related paper. Consider it for comparative context: