15 citations · 26 across the 7 of their papers we have counts for
7 papers
Periodic Trajectories and Topology of the Integrable Boltzmann System
Sean Gasiorek, Milena Radnović
We consider the Boltzmann system corresponding to the motion of a billiard with a linear boundary under the influence of a gravitational field. We derive analytic conditions of Cay…
Billiard Ordered Games and Books
Vladimir Dragovic, Sean Gasiorek, Milena Radnovic
The aim of this work is to put together two novel concepts from the theory of integrable billiards: billiard ordered games and confocal billiard books. Billiard books appeared rece…
Linear Stability of Periodic Trajectories in Inverse Magnetic Billiards
Sean Gasiorek
We study the stability of periodic trajectories of planar inverse magnetic billiards, a dynamical system whose trajectories are straight lines inside a connected planar domain …
Integrable Billiards on a Minkowski Hyperboloid: Extremal Polynomials and Topology
Vladimir Dragovic, Sean Gasiorek, Milena Radnovic
We consider billiard systems within compact domains bounded by confocal conics on a hyperboloid of one sheet in the Minkowski space. We derive conditions for elliptic periodicity f…
Pseudo-Euclidean Billiards within Confocal Curves on the Hyperboloid of One Sheet
Sean Gasiorek, Milena Radnovic
We consider a billiard problem for compact domains bounded by confocal conics on a hyperboloid of one sheet in the Minkowski space. We show that there are two types of confocal fam…
On the Dynamics of Inverse Magnetic Billiards
Sean Gasiorek
Consider a strictly convex set in the plane, and a homogeneous, stationary magnetic field orthogonal to the plane whose strength is on the complement of and inside…
Counting Collisions in an -Billiard System Using Angles Between Collision Subspaces
Sean Gasiorek
The principal angles between binary collision subspaces in an -billiard system in -dimensional Euclidean space are computed. These angles are computed for equal masses and ar…