On P-adic generalized logistic dynamical system
Applications of p-adic numbers in p-adic mathematical physics, quantum mechanics stimulated increasing interest in the study of p-adic dynamical system. One of the interesting p-adic dynamical system is p-adic logistic map. It is known such a mapping is chaotic. In the present paper, we consider its...
| Main Authors: | , |
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| Format: | Proceeding Paper |
| Language: | English |
| Published: |
2011
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| Subjects: | |
| Online Access: | http://irep.iium.edu.my/12729/1/isasm2011_3.pdf |
| _version_ | 1825645343496208384 |
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| author | Wan Rozali, Wan Nur Fairuz Alwani Mukhamedov, Farrukh |
| author_facet | Wan Rozali, Wan Nur Fairuz Alwani Mukhamedov, Farrukh |
| author_sort | Wan Rozali, Wan Nur Fairuz Alwani |
| collection | IIUM |
| description | Applications of p-adic numbers in p-adic mathematical physics, quantum mechanics stimulated increasing interest in the study of p-adic dynamical system. One of the interesting p-adic dynamical system is p-adic logistic map. It is known such a mapping is chaotic. In the present paper, we consider its cubic generalization namely we study a dynamical system of the form 2 f (x) ax(1 x ) .
The paper is devoted to the investigation of trajectory of the given system. We investigate the generalized logistic dynamical system with respect to parameter a. For the value of parameter, we consider the case when |a|p < 1. In this case, we study the existence of the fixed points and periodic points for every prime number, p. Not only that, their behavior also being investigated whether such fixed points and periodic points are attracting, repelling or neutral. Moreover, we describe the Siegel discs of the system, since the structure of the orbits of the system is related to the geometry of the p-adic Siegel discs. |
| first_indexed | 2024-03-05T22:46:18Z |
| format | Proceeding Paper |
| id | oai:generic.eprints.org:12729 |
| institution | International Islamic University Malaysia |
| language | English |
| last_indexed | 2024-03-05T22:46:18Z |
| publishDate | 2011 |
| record_format | dspace |
| spelling | oai:generic.eprints.org:127292011-12-30T03:11:48Z http://irep.iium.edu.my/12729/ On P-adic generalized logistic dynamical system Wan Rozali, Wan Nur Fairuz Alwani Mukhamedov, Farrukh QA Mathematics Applications of p-adic numbers in p-adic mathematical physics, quantum mechanics stimulated increasing interest in the study of p-adic dynamical system. One of the interesting p-adic dynamical system is p-adic logistic map. It is known such a mapping is chaotic. In the present paper, we consider its cubic generalization namely we study a dynamical system of the form 2 f (x) ax(1 x ) . The paper is devoted to the investigation of trajectory of the given system. We investigate the generalized logistic dynamical system with respect to parameter a. For the value of parameter, we consider the case when |a|p < 1. In this case, we study the existence of the fixed points and periodic points for every prime number, p. Not only that, their behavior also being investigated whether such fixed points and periodic points are attracting, repelling or neutral. Moreover, we describe the Siegel discs of the system, since the structure of the orbits of the system is related to the geometry of the p-adic Siegel discs. 2011-11 Proceeding Paper NonPeerReviewed application/pdf en http://irep.iium.edu.my/12729/1/isasm2011_3.pdf Wan Rozali, Wan Nur Fairuz Alwani and Mukhamedov, Farrukh (2011) On P-adic generalized logistic dynamical system. In: International Seminar on the Application of Science & Mathematics 2011, 1-3 November 2011, Kuala Lumpur. http://uhsb.uthm.edu.my/isasm2011/ISASM2011%20FULL%20PAPER.pdf |
| spellingShingle | QA Mathematics Wan Rozali, Wan Nur Fairuz Alwani Mukhamedov, Farrukh On P-adic generalized logistic dynamical system |
| title | On P-adic generalized logistic dynamical system |
| title_full | On P-adic generalized logistic dynamical system |
| title_fullStr | On P-adic generalized logistic dynamical system |
| title_full_unstemmed | On P-adic generalized logistic dynamical system |
| title_short | On P-adic generalized logistic dynamical system |
| title_sort | on p adic generalized logistic dynamical system |
| topic | QA Mathematics |
| url | http://irep.iium.edu.my/12729/1/isasm2011_3.pdf |
| work_keys_str_mv | AT wanrozaliwannurfairuzalwani onpadicgeneralizedlogisticdynamicalsystem AT mukhamedovfarrukh onpadicgeneralizedlogisticdynamicalsystem |