2 papers
math.DG2007
Converse Sturm-Hurwitz-Kellogg theorem and related results
S. Tabachnikov
The classical Sturm-Hurwitz-Kellogg theorem asserts that a function, orthogonal to an n-dimensional Chebyshev system on a circle, has at least n+1 sign changes. We prove the conver…
math.DS2007
On algebraically integrable outer billiards
S. Tabachnikov
We prove that if the outer billiard map around a plane oval is algebraically integrable in a certain non-degenerate sense then the oval is an ellipse.