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arXiv · 2008.07065

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

Shiping Cao·Malte S. Hassler·Hua Qiu·Ely Sandine·Robert S. Strichartz
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Abstract

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.

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Shiping Cao, Malte S. Hassler, Hua Qiu, Ely Sandine, Robert S. Strichartz. 2020-08-17. Existence and uniqueness of diffusions on the Julia sets of Misiurewicz-Sierpinski maps. https://arxiv.org/abs/2008.07065

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