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
Disconnected large bifurcation supports and Cartesian products of bifurcations
Timur Bakiev, Yulij S. Ilyashenko
A bifurcation that occurs in a multiparameter family is a Cartesian product if it splits into two factors in the sense that one bifurcation takes place in one part of the phase por…