3 papers
math.DS2026
Remarks on the outer length billiards
Misha Bialy, Serge Tabachnikov
We study outer length billiards; our main results are as follows. We prove 3- and 4-periodic versions of the Ivrii conjecture. We show that, for every period , there exists…
math.DG2006
On configuration spaces of plane polygons, sub-Riemannian geometry and periodic orbits of outer billiards
D. Genin, S. Tabachnikov
Following a recent paper by Baryshnikov and Zharnitskii, we consider outer billiards in the plane possessing invariant curves consisting of periodic orbits. We prove the existence…
math.DS2005
Complexity of piecewise convex transformations in two dimensions, with applications to polygonal billiards
E. Gutkin, S. Tabachnikov
We introduce the class of piecewise convex transformations, and study their complexity. We apply the results to the complexity of polygonal billiards on surfaces of constant curvat…