Weyl law for fat fractals
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.
 Publication:

arXiv eprints
 Pub Date:
 July 2010
 arXiv:
 arXiv:1007.2819
 Bibcode:
 2010arXiv1007.2819S
 Keywords:

 Nonlinear Sciences  Chaotic Dynamics;
 Quantum Physics
 EPrint:
 8 pages, 4 figures, IOP format