On dynamical system relating to quantum Markov chain associated with Ising Model on Cayley tree
In the present paper, we study stability of the dynamical system corresponding quantum Markov chain (QMC) associated with the Ising model on Cayley tree of order two. To study certain properties of QMC we reduce our investigation to the study of dynamics of a nonlinear dynamical system. For such a d...
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| Format: | Article |
| Language: | English |
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INSI Publications
2011
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| Online Access: | http://irep.iium.edu.my/1610/ http://irep.iium.edu.my/1610/1/mfms-AustJMS%282011%29.pdf |
| _version_ | 1848775883691655168 |
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| author | Mukhamedov, Farrukh Saburov, Mansoor |
| author_facet | Mukhamedov, Farrukh Saburov, Mansoor |
| author_sort | Mukhamedov, Farrukh |
| building | IIUM Repository |
| collection | Online Access |
| description | In the present paper, we study stability of the dynamical system corresponding quantum Markov chain (QMC) associated with the Ising model on Cayley tree of order two. To study certain properties of QMC we reduce our investigation to the study of dynamics of a nonlinear dynamical system. For such a dynamical system it is proved existence of exactly three fixed points and absence of periodic points. Moreover, it is established finiteness and infiniteness of the trajectory of the system. |
| first_indexed | 2025-11-14T14:21:17Z |
| format | Article |
| id | iium-1610 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T14:21:17Z |
| publishDate | 2011 |
| publisher | INSI Publications |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-16102012-12-28T06:31:40Z http://irep.iium.edu.my/1610/ On dynamical system relating to quantum Markov chain associated with Ising Model on Cayley tree Mukhamedov, Farrukh Saburov, Mansoor QA Mathematics In the present paper, we study stability of the dynamical system corresponding quantum Markov chain (QMC) associated with the Ising model on Cayley tree of order two. To study certain properties of QMC we reduce our investigation to the study of dynamics of a nonlinear dynamical system. For such a dynamical system it is proved existence of exactly three fixed points and absence of periodic points. Moreover, it is established finiteness and infiniteness of the trajectory of the system. INSI Publications 2011 Article PeerReviewed application/pdf en http://irep.iium.edu.my/1610/1/mfms-AustJMS%282011%29.pdf Mukhamedov, Farrukh and Saburov, Mansoor (2011) On dynamical system relating to quantum Markov chain associated with Ising Model on Cayley tree. Australian Journal of Basic and Applied Sciences, 5 (3). pp. 20-27. ISSN 1991-8178 http://www.insipub.com/ajbas_march_2011.html |
| spellingShingle | QA Mathematics Mukhamedov, Farrukh Saburov, Mansoor On dynamical system relating to quantum Markov chain associated with Ising Model on Cayley tree |
| title | On dynamical system relating to quantum Markov chain associated with Ising Model on Cayley tree |
| title_full | On dynamical system relating to quantum Markov chain associated with Ising Model on Cayley tree |
| title_fullStr | On dynamical system relating to quantum Markov chain associated with Ising Model on Cayley tree |
| title_full_unstemmed | On dynamical system relating to quantum Markov chain associated with Ising Model on Cayley tree |
| title_short | On dynamical system relating to quantum Markov chain associated with Ising Model on Cayley tree |
| title_sort | on dynamical system relating to quantum markov chain associated with ising model on cayley tree |
| topic | QA Mathematics |
| url | http://irep.iium.edu.my/1610/ http://irep.iium.edu.my/1610/ http://irep.iium.edu.my/1610/1/mfms-AustJMS%282011%29.pdf |