Some strange properties of quadratic stochastic volterra operators
One of the fascinating results in the one dimensional nonlinear dynamical system is that a mapping which maps a compact connected subset of the real line into itself is regular if and only if it does not have any order periodic points except fixed points. However, in general, this result does not ho...
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| Format: | Article |
| Language: | English |
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IDOSI Publication
2012
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| Online Access: | http://irep.iium.edu.my/27937/ http://irep.iium.edu.my/27937/1/Strange_Properties_V-QSO-WASJ.pdf |
| _version_ | 1848779894532603904 |
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| author | Saburov, Mansoor |
| author_facet | Saburov, Mansoor |
| author_sort | Saburov, Mansoor |
| building | IIUM Repository |
| collection | Online Access |
| description | One of the fascinating results in the one dimensional nonlinear dynamical system is that a mapping which maps a compact connected subset of the real line into itself is regular if and only if it does not have any order periodic points except fixed points. However, in general, this result does not hold true in the high dimensional case. In this paper, we provide a counter example for such kind of mappings among quadratic stochastic Volterra operators. Moreover, we showed an equivalence of notions of regularity,
transitivity and Ergodic principle for quadratic stochastic Volterra operators acting on the finite dimensional
simplex. Apart from these, we study the fixed point set of the composition of two quadratic stochastic Volterra
operators. |
| first_indexed | 2025-11-14T15:25:02Z |
| format | Article |
| id | iium-27937 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T15:25:02Z |
| publishDate | 2012 |
| publisher | IDOSI Publication |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-279372013-04-23T02:55:27Z http://irep.iium.edu.my/27937/ Some strange properties of quadratic stochastic volterra operators Saburov, Mansoor QA Mathematics One of the fascinating results in the one dimensional nonlinear dynamical system is that a mapping which maps a compact connected subset of the real line into itself is regular if and only if it does not have any order periodic points except fixed points. However, in general, this result does not hold true in the high dimensional case. In this paper, we provide a counter example for such kind of mappings among quadratic stochastic Volterra operators. Moreover, we showed an equivalence of notions of regularity, transitivity and Ergodic principle for quadratic stochastic Volterra operators acting on the finite dimensional simplex. Apart from these, we study the fixed point set of the composition of two quadratic stochastic Volterra operators. IDOSI Publication 2012 Article PeerReviewed application/pdf en http://irep.iium.edu.my/27937/1/Strange_Properties_V-QSO-WASJ.pdf Saburov, Mansoor (2012) Some strange properties of quadratic stochastic volterra operators. World Applied Sciences Journal , 20. pp. 94-97. ISSN 1818-4952 http://iosrjournals.org/ 10.5829/idosi.wasj.2012.20.mae.99929 |
| spellingShingle | QA Mathematics Saburov, Mansoor Some strange properties of quadratic stochastic volterra operators |
| title | Some strange properties of quadratic stochastic volterra operators |
| title_full | Some strange properties of quadratic stochastic volterra operators |
| title_fullStr | Some strange properties of quadratic stochastic volterra operators |
| title_full_unstemmed | Some strange properties of quadratic stochastic volterra operators |
| title_short | Some strange properties of quadratic stochastic volterra operators |
| title_sort | some strange properties of quadratic stochastic volterra operators |
| topic | QA Mathematics |
| url | http://irep.iium.edu.my/27937/ http://irep.iium.edu.my/27937/ http://irep.iium.edu.my/27937/ http://irep.iium.edu.my/27937/1/Strange_Properties_V-QSO-WASJ.pdf |