Add to ORKGWe prove that any sufficiently small perturbation of an isosceles triangle has a peri-odic billiard path. Our proof involves the analysis of certain infinite families of Fourier series that arise in connection with triangular billiards, and reveals some self-similarity phenomena in irrational triangular billiards. Our analysis illustrates the surprising fact that billiards on a triangle near a Veech triangle is extremely complicated even though billiards on a Veech triangle is very well understood.
We develop a framework for dealing with smooth approximations to billiards with corners in the two-d...
We consider an outer billiard around a Reulaux triangle. We prove the existence of infinitely many p...
In the 20th century, mathematicians studied the motion of particles with elastic collisions (called ...
We give a rigorous computer-assisted proof that a triangle has a periodic billiard path provided all...
We provide a complete characterization of billiard trajectory hitting sequences () () on [pi] -isosc...
47 pages, 18 figuresInternational audienceConsider a periodic tiling of a plane by equal triangles o...
Let Sǫ denote the set of Euclidean triangles whose two small angles are within ǫ radians of π6 and π...
We prove some recent experimental observations of Dan Reznik concerning periodic billiard orbits in ...
Abstract. A periodic trajectory on a polygonal billiard table is stable if it persists under any suf...
Mathematical billiards describe the motion of a mass point in a domain with elastic reflections off ...
Abstract: We consider an outer billiard around a Reulaux triangle. We prove the existence of infinit...
Billiard maps are a type of area-preserving twist maps and, thus, they inherit a vast num-ber of pro...
In our recent paper [1], we studied periodic billiard trajectories in a regular pentagon and in the ...
Abstract. Given a strictly convex domain Ω ⊂ R2, there is a natural way to define a billiard map in ...
In this dissertation, we will focus our attention on the limiting behavior of a sequence of compatib...
We develop a framework for dealing with smooth approximations to billiards with corners in the two-d...
We consider an outer billiard around a Reulaux triangle. We prove the existence of infinitely many p...
In the 20th century, mathematicians studied the motion of particles with elastic collisions (called ...
We give a rigorous computer-assisted proof that a triangle has a periodic billiard path provided all...
We provide a complete characterization of billiard trajectory hitting sequences () () on [pi] -isosc...
47 pages, 18 figuresInternational audienceConsider a periodic tiling of a plane by equal triangles o...
Let Sǫ denote the set of Euclidean triangles whose two small angles are within ǫ radians of π6 and π...
We prove some recent experimental observations of Dan Reznik concerning periodic billiard orbits in ...
Abstract. A periodic trajectory on a polygonal billiard table is stable if it persists under any suf...
Mathematical billiards describe the motion of a mass point in a domain with elastic reflections off ...
Abstract: We consider an outer billiard around a Reulaux triangle. We prove the existence of infinit...
Billiard maps are a type of area-preserving twist maps and, thus, they inherit a vast num-ber of pro...
In our recent paper [1], we studied periodic billiard trajectories in a regular pentagon and in the ...
Abstract. Given a strictly convex domain Ω ⊂ R2, there is a natural way to define a billiard map in ...
In this dissertation, we will focus our attention on the limiting behavior of a sequence of compatib...
We develop a framework for dealing with smooth approximations to billiards with corners in the two-d...
We consider an outer billiard around a Reulaux triangle. We prove the existence of infinitely many p...
In the 20th century, mathematicians studied the motion of particles with elastic collisions (called ...