00-148 Lowenstein J. H., Vivaldi F.

Embedding dynamics for round-off errors near a periodic orbit. (1165K, postscript) Apr 4, 00

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Abstract. We study the propagation of round-off errors near the periodic orbits of a linear map conjugate to a planar rotation with rational rotation number. We embed the two-dimensional discrete phase space (a lattice) in a higher-dimensional torus, where points sharing the same round-off error are uniformly distributed within finitely many convex polyhedra. The embedding dynamics is linear and discontinuous, with algebraic integer parameters. This representation affords efficient algorithms for classifying and computing the orbits and their densities, which we apply to the case of rational rotation number with denominator 7, corresponding to certain algebraic integers of degree three. We provide evidence that the hierarchical arrangement of orbits previously detected in quadratic cases disappears, and that the growth of the number of orbits with the period is algebraic.

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