arXiv subjects

Malte S. Hassler

Publications and source records attributed to Malte S. Hassler.

2 recordsLinked to original sources

arXiv2020

Existence and uniqueness of diffusions on the Julia sets of Misiurewicz-Sierpinski maps

We study the balanced resistance forms on the Julia sets of Misiurewicz-Sierpinski maps, which are self-similar resistance forms with equal weights. In particular, we use a theorem of Sabot to prove the existence and uniqueness of balanced forms on these Julia sets. We also provide an explorative study on the resistance forms on the Julia sets of rational maps with periodic critical points.

math.FA↗

arXiv2020

Laplacians on Julia sets of rational maps

The study of Julia sets gives a new and natural way to look at fractals. When mathematicians investigated the special class of Misiurewicz's rational maps, they found out that there is a Julia set which is homeomorphic to a well known fractal, the Sierpinski gasket. In this paper, we apply the method of Kigami to give rise to a new construction of Laplacians on the Sierpinski gasket like Julia sets with a dynamically invariant property.

math.DS↗