Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8904494 | Acta Mathematica Scientia | 2017 | 16 Pages |
Abstract
We give heat kernel estimates on Julia sets J(fc) for quadratic polynomials fc(z)= z2 + c for c in the main cardioid or the
±1k-bulbs where k â¥2. First we use external ray parametrization to construct a regular, strongly local and conservative Dirichlet form on Julia set. Then we show that this Dirichlet form is a resistance form and the corresponding resistance metric induces the same topology as Euclidean metric. Finally, we give heat kernel estimates under the resistance metric.
Keywords
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Meng YANG,