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满足开集条件的自相似集的Lipschitz等价
  • ISSN号：1000-8314
  • 期刊名称：数学年刊A辑(中文版)
  • 时间：2012
  • 页码：1-16
  • 分类：O18[理学—数学;理学—基础数学]
  • 作者机构：[1]华南理工大学数学系,广州510641, [2]浙江万里学院数学研究所,浙江宁波315100
  • 相关基金：国家申然科学基金（No.11101159,No.11071124,No.11071082）,新世纪优秀人才支持计划,中央高校科研基本业务费（No.2009ZM0216）,高等学校博士学科点专项科研基金（No.20100172120027）和晨兴数学中心资助的项目.
  • 相关项目：基于几何群论与图灵机观点的分形研究
作者： 熊瑛|奚李峰|
关键词： LIPSCHITZ等价, 自相似集, 开集条件, Lipschitz equivalence, Self-similar set, Open set condition
中文摘要：

固定r∈（0，1）及整数N≥2，设E和E’为由N个形如s（z）=±rx＋b的压缩映射所生成的自相似集．设开集条件对于E及E’成立，并且所对应的开集为开区间，证明了E和E’Lipschitz等价．

英文摘要：

Fix r E （0, 1） and an integer N≥2. Let E and E＇ be self-similar sets generated by N contraction mappings of the form S（x） = ±rx ＋ b. Suppose that open set conditions hold for E and E＇, where the corresponding open sets are open intervals, then E and E＇ are Lipschitz equivalent.

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期刊信息
  • 《数学年刊：A辑》
  • 中国科技核心期刊
  • 主管单位:国家教育部
  • 主办单位:复旦大学
  • 主编：李大潜
  • 地址：上海市长乐路746号
  • 邮编：200040
  • 邮箱：edcam@fudan.edu.cn
  • 电话：021-65642338
  • 国际标准刊号：ISSN：1000-8314
  • 国内统一刊号：ISSN：31-1328/O1
  • 邮发代号:4-298
  • 获奖情况:
  • 国内外数据库收录:
  • 俄罗斯文摘杂志,美国数学评论（网络版）,德国数学文摘,中国中国科技核心期刊,中国北大核心期刊（2004版）,中国北大核心期刊（2008版）,中国北大核心期刊（2011版）,中国北大核心期刊（2014版）,中国北大核心期刊（2000版）
  • 被引量:4264