HEAT KERNEL ESTIMATES ON JULIA SETS

doi:10.1016/S0252-9602(17)30081-4

Abstract

Abstract:

We give heat kernel estimates on Julia sets J (f_c) for quadratic polynomials f_c (z)=z²+c for c in the main cardioid or the ±(1)/k-bulbs where k ≥ 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.

Key words: Julia sets, heat kernel, resistance metric

Meng YANG. HEAT KERNEL ESTIMATES ON JULIA SETS[J].Acta mathematica scientia,Series B, 2017, 37(5): 1399-1414.

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