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Graph-Directed Self-Similar Set in Complete Metric Spaces(PDF)

《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

Issue:
2016年02期
Page:
16-
Research Field:
数学
Publishing date:

Info

Title:
Graph-Directed Self-Similar Set in Complete Metric Spaces
Author(s):
Wei Min1; Yan Zhenzhen2; Shi Lei1
（1.College of Sciences，Nanjing Agricultural University，Nanjing 210095，China）（2.College of Science，Nanjing University of Posts and Telecommunications，Nanjing 210046，China）
Keywords:
graph-directed self-similar sets; open set condition（OSC）; strong open set condition（SOSC）
PACS:
O19
DOI:
10.3969/j.issn.1001-4616.2016.02.004
Abstract:
In this topic，we develop the Hausdorff dimension，Hausdorff measure of graph-directed self-similar sets in complete metric spaces. These are different from Rd，that is to say，the sets satisfy OSC in Rd，but we cannot have the conclusion that the [α]dimensional Hausdorff measure of graph-directed self-similar set K is positive in complete metric spaces，where the [α]is the Hausdorff dimension of K. We find the relationship between strong open set condition，Hausdorff dimension，the positivity of the Hausdorff measure and [β]space of graph-directed self-similar sets in complete metric spaces.

References:

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Memo

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Last Update: 2016-06-30