On metric properties of unconventional limit sets of contractive non-Archimedean dynamical systems
In this paper, we define the limit set Λξ of an unconventional set of contractive functions {fk} on the unit ball of non-Archimedean algebra. Then, we prove that Λξ is compact, perfect and uniformly disconnected. It is shown that there is a new collection of contractive mappings (Formula presented.)...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English English |
| Published: |
Taylor and Francis Ltd.
2016
|
| Subjects: | |
| Online Access: | http://irep.iium.edu.my/58860/ http://irep.iium.edu.my/58860/ http://irep.iium.edu.my/58860/ http://irep.iium.edu.my/58860/1/58860_On%20metric%20properties%20of%20unconventional_article.pdf http://irep.iium.edu.my/58860/2/58860_On%20metric%20properties%20of%20unconventional_scopus.pdf |
| id |
iium-58860 |
|---|---|
| recordtype |
eprints |
| spelling |
iium-588602017-10-22T03:12:34Z http://irep.iium.edu.my/58860/ On metric properties of unconventional limit sets of contractive non-Archimedean dynamical systems Mukhamedov, Farrukh M. Khakimov, Otabek Kh Q Science (General) QA Mathematics In this paper, we define the limit set Λξ of an unconventional set of contractive functions {fk} on the unit ball of non-Archimedean algebra. Then, we prove that Λξ is compact, perfect and uniformly disconnected. It is shown that there is a new collection of contractive mappings (Formula presented.) defined on Λξ. Moreover, we establish that the set Λξ coincides with the limit set generated by the semi-group of (Formula presented.). This result allows us to further investigate the structure of Λξ by means of this limiting set. As an application, we demonstrate the existence of invariant measures on Λξ. We should stress that the non-Archimedeanity of the space is essentially used in the paper. Therefore, the methods applied in this paper are not longer valid in the Archimedean setting (i.e. in case of real or complex numbers). Taylor and Francis Ltd. 2016-10 Article PeerReviewed application/pdf en http://irep.iium.edu.my/58860/1/58860_On%20metric%20properties%20of%20unconventional_article.pdf application/pdf en http://irep.iium.edu.my/58860/2/58860_On%20metric%20properties%20of%20unconventional_scopus.pdf Mukhamedov, Farrukh M. and Khakimov, Otabek Kh (2016) On metric properties of unconventional limit sets of contractive non-Archimedean dynamical systems. Dynamical Systems, 31 (4). pp. 506-524. ISSN 1468-9367 http://www.tandfonline.com/doi/abs/10.1080/14689367.2016.1158241?journalCode=cdss20 10.1080/14689367.2016.1158241 |
| repository_type |
Digital Repository |
| institution_category |
Local University |
| institution |
International Islamic University Malaysia |
| building |
IIUM Repository |
| collection |
Online Access |
| language |
English English |
| topic |
Q Science (General) QA Mathematics |
| spellingShingle |
Q Science (General) QA Mathematics Mukhamedov, Farrukh M. Khakimov, Otabek Kh On metric properties of unconventional limit sets of contractive non-Archimedean dynamical systems |
| description |
In this paper, we define the limit set Λξ of an unconventional set of contractive functions {fk} on the unit ball of non-Archimedean algebra. Then, we prove that Λξ is compact, perfect and uniformly disconnected. It is shown that there is a new collection of contractive mappings (Formula presented.) defined on Λξ. Moreover, we establish that the set Λξ coincides with the limit set generated by the semi-group of (Formula presented.). This result allows us to further investigate the structure of Λξ by means of this limiting set. As an application, we demonstrate the existence of invariant measures on Λξ. We should stress that the non-Archimedeanity of the space is essentially used in the paper. Therefore, the methods applied in this paper are not longer valid in the Archimedean setting (i.e. in case of real or complex numbers). |
| format |
Article |
| author |
Mukhamedov, Farrukh M. Khakimov, Otabek Kh |
| author_facet |
Mukhamedov, Farrukh M. Khakimov, Otabek Kh |
| author_sort |
Mukhamedov, Farrukh M. |
| title |
On metric properties of unconventional limit sets of contractive non-Archimedean dynamical systems |
| title_short |
On metric properties of unconventional limit sets of contractive non-Archimedean dynamical systems |
| title_full |
On metric properties of unconventional limit sets of contractive non-Archimedean dynamical systems |
| title_fullStr |
On metric properties of unconventional limit sets of contractive non-Archimedean dynamical systems |
| title_full_unstemmed |
On metric properties of unconventional limit sets of contractive non-Archimedean dynamical systems |
| title_sort |
on metric properties of unconventional limit sets of contractive non-archimedean dynamical systems |
| publisher |
Taylor and Francis Ltd. |
| publishDate |
2016 |
| url |
http://irep.iium.edu.my/58860/ http://irep.iium.edu.my/58860/ http://irep.iium.edu.my/58860/ http://irep.iium.edu.my/58860/1/58860_On%20metric%20properties%20of%20unconventional_article.pdf http://irep.iium.edu.my/58860/2/58860_On%20metric%20properties%20of%20unconventional_scopus.pdf |
| first_indexed |
2023-09-18T21:23:17Z |
| last_indexed |
2023-09-18T21:23:17Z |
| _version_ |
1777412025095290880 |