title: Parameter dependence of stochastic layers in a quasicrystalline web.
abstract: Stochastic web maps with approximate quasicrystalline symmetry possess an infinite number of inequivalent fixed points embedded in stochastic layers of varying thickness. In this investigation exploratory steps are taken toward a systematic numerical determination of the widths of the stochastic layers as a function of the web map's control parameter. The study concentrates on a particular stochastic layer in the approximately fivefold symmetric web. Computer graphics and a simple stretching-and-folding criterion provide a coarse view, which is supplemented at finer scales by Greene's residue method. The exact reflection symmetries of invariant sets, as well as a five-dimensional representation of the map, are exploited to improve numerical precision. As the control parameter varies, one finds not only variations expected from island chain structures, but also larger-scale oscillations whose origin is not understood.
authors.affiliation: Department of Physics, New York University, New York, New York 10003.
authors.forename: J. H.
authors.initials: JH
authors.lastname: Lowenstein