HEAT KERNEL ESTIMATES ON JULIA SETS

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

数学物理学报(英文版) ›› 2017, Vol. 37 ›› Issue (5): 1399-1414.doi: 10.1016/S0252-9602(17)30081-4

HEAT KERNEL ESTIMATES ON JULIA SETS

杨甍

Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China

收稿日期:2016-01-08 修回日期:2017-04-27 出版日期:2017-10-25 发布日期:2017-10-25
作者简介:Meng YANG,E-mail:meng-yang13@mails.tsinghua.edu.cn

HEAT KERNEL ESTIMATES ON JULIA SETS

Meng YANG

Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China

Received:2016-01-08 Revised:2017-04-27 Online:2017-10-25 Published:2017-10-25

摘要/Abstract

摘要：

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.

关键词: Julia sets, heat kernel, resistance metric

Abstract:

Key words: Julia sets, heat kernel, resistance metric

杨甍. HEAT KERNEL ESTIMATES ON JULIA SETS[J]. 数学物理学报(英文版), 2017, 37(5): 1399-1414.

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

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HEAT KERNEL ESTIMATES ON JULIA SETS

HEAT KERNEL ESTIMATES ON JULIA SETS

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