Lowenstein J. H., Vivaldi F.
Embedding dynamics for round-off errors near a periodic orbit.
(1165K, postscript)
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.