  Cycle expansions are an efficient scheme for computing the properties of
chaotic systems. When enumerating the orbits for a cycle expansion not all
orbits that one would expect at first are present --- some are pruned. This
pruning leads to convergence difficulties when computing properties of chaotic
systems. In numerical schemes, I show that pruning reduces the number of
reliable eigenvalues when diagonalizing quantum mechanical operators, and that
pruning slows down the convergence rate of cycle expansion calculations. I then
exactly solve a diffusion model that displays chaos and show that its cycle
expansion develops a branch point.

Chaotic Dynamics;Chaotic Dynamics