2 papers
math.DS2026
Billiard maps of confocal ellipses commute: a geometric proof
Timur Bakiev, Ivan Molodyk
We give a new, purely geometric proof of the classical fact that billiard maps in confocal ellipses commute. Existing proofs of this result rely on symplectic geometry and an invar…
math.DS2025
On the Complexity of Bicycle Unitracks
Ivan Molodyk
This paper concerns the geometry of bicycle tracks. We model bicycle as an oriented segment of a fixed length that is moving in the Euclidean plane so that the trajectory of the re…