On a generalized self-similarity in the p-Adic field
In the present paper, we introduce a new set which defines a generalized self-similar set for contractive functions {fi}i=1N on the unit ball â&;p of p-Adic numbers. This set is called unconventional limit set. We prove that the unconventional limit set is compact, perfect and uniformly disconne...
| Main Authors: | , |
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| Format: | Article |
| Language: | English English |
| Published: |
World Scientific Publishing Co. Pte Ltd
2016
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| Subjects: | |
| Online Access: | http://irep.iium.edu.my/58854/ http://irep.iium.edu.my/58854/ http://irep.iium.edu.my/58854/ http://irep.iium.edu.my/58854/1/58854_On%20a%20generalized%20self-similarity%20in%20the%20p-Adic%20field_article.pdf http://irep.iium.edu.my/58854/2/58854_On%20a%20generalized%20self-similarity%20in%20the%20p-Adic%20field_scopus.pdf |
| Summary: | In the present paper, we introduce a new set which defines a generalized self-similar set for contractive functions {fi}i=1N on the unit ball â&;p of p-Adic numbers. This set is called unconventional limit set. We prove that the unconventional limit set is compact, perfect and uniformly disconnected. Moreover, we provide an example of two contractions for which the corresponding unconventional limiting set is quasi-symmetrically equivalent to the symbolic Cantor set. |
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