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

《南京师范大学学报》(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 Min1Yan Zhenzhen2Shi 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 setsopen 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