In this chapter we briefly give the theory (without proofs) of discrete and continuous-time
dynamical systems. This will be helpful for the reader, because a mathematical billiard which …

Obtuse Triangular Billiards II: One Hundred Degrees Worth of Periodic Trajectories Page 1
Obtuse Triangular Billiards II: One Hundred Degrees Worth of Periodic Trajectories Richard …

This is an updated and expanded version of our earlier survey article [E. Gutkin,“Billiard
dynamics: a survey with the emphasis on open problems,” Regular Chaotic Dyn. 8, 1–13 …

We describe a family Ψ α, β of polygon exchange transformations parameterized by points
(α, β) in the square 0,12*0,12. Whenever α and β are irrational, Ψ α, β has periodic orbits of …

Survey lecture on billiards Page 1 Survey lecture on billiards Richard Evan Schwartz Abstract
In this survey of billiards, I will discuss a variety of topics: rational polygonal billiards, irrational …

The orbit closure of the unfolding of every rational right and isosceles triangle is computed
and the asymptotic number of periodic billiard trajectories in these triangles is deduced. This …

Mathematical billiards is much like the real game: a point mass, representing the ball, rolls in
a straight line on a (perfectly friction-less) table, striking the sides according to the law of …

Differential drive robots, such as robotic vacuums, often have at least two motion primitives:
the ability to travel forward in straight lines, and rotate in place upon encountering a …

Under the current trend of automation development, in view of the fact that billiards requires
a special person to fetch the ball, the tedious labor of putting the ball has also been …

We define a moduli space of translation structures on the open topological disk with a
basepoint and endow it with a locally-compact metrizable topology. We call this the …