title: Critical states and fractal attractors in fractal tongues: localization in the Harper map.
abstract: Localized states of Harper's equation correspond to strange nonchaotic attractors in the related Harper mapping. In parameter space, these fractal attractors with nonpositive Lyapunov exponents occur in fractally organized tongue-like regions which emanate from the Cantor set of eigenvalues on the critical line epsilon=1. A topological invariant characterizes wave functions corresponding to energies in the gaps in the spectrum. This permits a unique integer labeling of the gaps and also determines their scaling properties as a function of potential strength.
authors.affiliation: School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110 067, India.
authors.forename: S S
authors.initials: SS
authors.lastname: Negi
authors.forename: R
authors.initials: R
authors.lastname: Ramaswamy