Coding of billiards in hyperbolic 3-space

Pradeep Singh

Abstract:

In this article, we produce the coding rules of billiards for a class of ideal polyhedrons
in the 3-dimensional hyperbolic space. Building on it, further we establish conjugacy
between the space of pointed billiard trajectories and the corresponding shift space of
codes. This opens up a direct route to study the related geometric properties via the
analytical tools available in Symbolic Dynamics.