Weyl law for fat fractals

Details Weyl law for fat fractals Weyl law for fat fractals

2010-07-16

arxiv.org/abs/1007.2819v1

J. Phys. A: Math. Theor. 43 (2010) 392003

Nonlinear Sciences

Chaotic Dynamics

8 pages, 4 figures, IOP format

Scientific paper

10.1088/1751-8113/43/39/392003

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.

Affiliated with

Also associated with

No associations

Rating

Weyl law for fat fractals does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Weyl law for fat fractals, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Weyl law for fat fractals will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-51677