期刊
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
卷 51, 期 -, 页码 160-168出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cnsns.2017.04.009
关键词
Self similar set; Open set condition; Similarity dimension; Hausdorff dimension
The separation properties of self similar sets are discussed in this article. An open set condition for the (n, m)- iterated function system is introduced and the concepts of self similarity, similarity dimension and Hausdorff dimension of the attractor generated by an (n, m) - iterated function system are studied. It is proved that the similarity dimension and the Hausdorff dimension of the attractor of an (n, m) - iterated function system are equal under this open set condition. Further a necessary and sufficient condition for a set to satisfy the open set condition is established. (C) 2017 Elsevier B.V. All rights reserved.
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