Preprint D43/2007
Growth rates for geometric complexities and counting functions
Michal Rams | Gutkin, Eugene
Keywords: Geodesic polygon | billiard map | billiard flow | complexity | counting functions | unfolding of orbits | covering space | exponential map
We introduce a new method for estimating the growth of various quantities arising in dynamical systems. We apply our method to polygonal billiards on surfaces of constant curvature. For instance, we obtain power bounds of degree two plus epsilon in length for the number of billiard orbits between almost all pairs of points in a planar polygon.