On non-ergodic volterra cubic stochastic operators
Let Sm−1 be the simplex in Rm , and V:Sm−1→Sm−1 be a nonlinear mapping then this operator satisfies an ergodic theorem if the limit limn→∞1n∑k=1nVk(x) exists for every x∈Sm−1 . It is a well known fact that this ergodicity may fail for Volterra quadratic operators, so it is natural to char...
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Springer
2019
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| Online Access: | http://irep.iium.edu.my/73972/ http://irep.iium.edu.my/73972/1/73972_On%20Non-ergodic%20Volterra%20Cubic%20Stochastic_article.pdf http://irep.iium.edu.my/73972/2/73972_On%20Non-ergodic%20Volterra%20Cubic%20Stochastic_scopus.pdf http://irep.iium.edu.my/73972/3/73972_On%20Non-ergodic%20Volterra%20Cubic%20Stochastic_wos.pdf |
| _version_ | 1848787889107763200 |
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| author | Mukhamedov, Farrukh Pah, Chin Hee Rosli, Azizi |
| author_facet | Mukhamedov, Farrukh Pah, Chin Hee Rosli, Azizi |
| author_sort | Mukhamedov, Farrukh |
| building | IIUM Repository |
| collection | Online Access |
| description | Let Sm−1 be the simplex in Rm , and V:Sm−1→Sm−1 be a nonlinear mapping then this operator satisfies an ergodic theorem if the limit
limn→∞1n∑k=1nVk(x) exists for every x∈Sm−1 . It is a well known fact that this ergodicity may fail for Volterra quadratic operators, so it is natural to characterize all non-ergodic operators. However, there is an ongoing problem even in the low dimensional simplexes. In this paper, we solve the mentioned problem within Volterra cubic stochastic operators acting on two-dimensional simplex. |
| first_indexed | 2025-11-14T17:32:06Z |
| format | Article |
| id | iium-73972 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English English English |
| last_indexed | 2025-11-14T17:32:06Z |
| publishDate | 2019 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-739722020-04-05T09:21:36Z http://irep.iium.edu.my/73972/ On non-ergodic volterra cubic stochastic operators Mukhamedov, Farrukh Pah, Chin Hee Rosli, Azizi QA Mathematics Let Sm−1 be the simplex in Rm , and V:Sm−1→Sm−1 be a nonlinear mapping then this operator satisfies an ergodic theorem if the limit limn→∞1n∑k=1nVk(x) exists for every x∈Sm−1 . It is a well known fact that this ergodicity may fail for Volterra quadratic operators, so it is natural to characterize all non-ergodic operators. However, there is an ongoing problem even in the low dimensional simplexes. In this paper, we solve the mentioned problem within Volterra cubic stochastic operators acting on two-dimensional simplex. Springer 2019 Article PeerReviewed application/pdf en http://irep.iium.edu.my/73972/1/73972_On%20Non-ergodic%20Volterra%20Cubic%20Stochastic_article.pdf application/pdf en http://irep.iium.edu.my/73972/2/73972_On%20Non-ergodic%20Volterra%20Cubic%20Stochastic_scopus.pdf application/pdf en http://irep.iium.edu.my/73972/3/73972_On%20Non-ergodic%20Volterra%20Cubic%20Stochastic_wos.pdf Mukhamedov, Farrukh and Pah, Chin Hee and Rosli, Azizi (2019) On non-ergodic volterra cubic stochastic operators. Qualitative Theory of Dynamical Systems. ISSN 1575-5460 E-ISSN 1662-3592 (In Press) https://link.springer.com/article/10.1007/s12346-019-00334-8 10.1007/s12346-019-00334-8 |
| spellingShingle | QA Mathematics Mukhamedov, Farrukh Pah, Chin Hee Rosli, Azizi On non-ergodic volterra cubic stochastic operators |
| title | On non-ergodic volterra cubic stochastic operators |
| title_full | On non-ergodic volterra cubic stochastic operators |
| title_fullStr | On non-ergodic volterra cubic stochastic operators |
| title_full_unstemmed | On non-ergodic volterra cubic stochastic operators |
| title_short | On non-ergodic volterra cubic stochastic operators |
| title_sort | on non-ergodic volterra cubic stochastic operators |
| topic | QA Mathematics |
| url | http://irep.iium.edu.my/73972/ http://irep.iium.edu.my/73972/ http://irep.iium.edu.my/73972/ http://irep.iium.edu.my/73972/1/73972_On%20Non-ergodic%20Volterra%20Cubic%20Stochastic_article.pdf http://irep.iium.edu.my/73972/2/73972_On%20Non-ergodic%20Volterra%20Cubic%20Stochastic_scopus.pdf http://irep.iium.edu.my/73972/3/73972_On%20Non-ergodic%20Volterra%20Cubic%20Stochastic_wos.pdf |