Weyl law for fat fractals
Chaotic Dynamics
2010-09-02 v1 Quantum Physics
Abstract
It has been conjectured that for a class of piecewise linear maps the closure of the set of images of the discontinuity has the structure of a fat fractal, that is, a fractal with positive measure. An example of such maps is the sawtooth map in the elliptic regime. In this work we analyze this problem quantum mechanically in the semiclassical regime. We find that the fraction of states localized on the unstable set satisfies a modified fractal Weyl law, where the exponent is given by the exterior dimension of the fat fractal.
Keywords
Cite
@article{arxiv.1007.2819,
title = {Weyl law for fat fractals},
author = {Maria E. Spina and Ignacio Garcia-Mata and Marcos Saraceno},
journal= {arXiv preprint arXiv:1007.2819},
year = {2010}
}
Comments
8 pages, 4 figures, IOP format