title: Quasi-periodicity, global stability and scaling in a model of Hamiltonian round-off.
abstract: We investigate the effects of round-off errors on the orbits of a linear symplectic map of the plane, with rational rotation number nu=p/q. Uniform discretization transforms this map into a permutation of the integer lattice Z(2). We study in detail the case q=5, exploiting the correspondence between Z and a suitable domain of algebraic integers. We completely classify the orbits, proving that all of them are periodic. Using higher-dimensional embedding, we establish the quasi-periodicity of the phase portrait. We show that the model exhibits asymptotic scaling of the periodic orbits and a long-range clustering property similar to that found in repetitive tilings of the plane. (c) 1997 American Institute of Physics.
authors.affiliation: School of Mathematical Sciences, Queen Mary and Westfield College, Mile End Road, London E1 4NS, England.
authors.forename: John
authors.initials: J
authors.lastname: Lowenstein
authors.forename: Spyros
authors.initials: S
authors.lastname: Hatjispyros
authors.forename: Franco
authors.initials: F
authors.lastname: Vivaldi