CYCLE EXPANSIONS WITH PRUNED ORBITS HAVE BRANCH-POINTS

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 p runed. This pruning leads to convergence difficulties when computing p roperties of chaotic systems. In numerical schemes. I show that prunin g reduces the number of reliable eigenvalues when diagonalizing quantu m mechanical operators, and that pruning slows down the convergence ra te of cycle expansion calculations. I then exactly solve a diffusion m odel that displays chaos and show that its cycle expansion develops a branch point.