Cycle expansions with pruned orbits have branch points

Details Cycle expansions with pruned orbits have branch points Cycle expansions with pruned orbits have branch points

1994-12-15

arxiv.org/abs/chao-dyn/9412008v1

Nonlinear Sciences

Chaotic Dynamics

17 pages and 9 figures in 183364 bytes of uuencoded compressed PostScript

Scientific paper

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.

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