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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iium-739722019-09-11T01:05:42Z 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/73972/8/73972%20On%20Non-ergodic%20Volterra%20Cubic%20-In-press.pdf application/pdf en http://irep.iium.edu.my/73972/9/73972%20On%20Non-ergodic%20Volterra%20Cubic%20-In-press%20SCOPUS%20pdf.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 |
| repository_type |
Digital Repository |
| institution_category |
Local University |
| institution |
International Islamic University Malaysia |
| building |
IIUM Repository |
| collection |
Online Access |
| language |
English English |
| topic |
QA Mathematics |
| spellingShingle |
QA Mathematics Mukhamedov, Farrukh Pah, Chin Hee Rosli, Azizi On non-ergodic volterra cubic stochastic operators |
| 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. |
| format |
Article |
| author |
Mukhamedov, Farrukh Pah, Chin Hee Rosli, Azizi |
| author_facet |
Mukhamedov, Farrukh Pah, Chin Hee Rosli, Azizi |
| author_sort |
Mukhamedov, Farrukh |
| title |
On non-ergodic volterra cubic stochastic operators |
| title_short |
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_sort |
on non-ergodic volterra cubic stochastic operators |
| publisher |
Springer |
| publishDate |
2019 |
| url |
http://irep.iium.edu.my/73972/ http://irep.iium.edu.my/73972/ http://irep.iium.edu.my/73972/ http://irep.iium.edu.my/73972/8/73972%20On%20Non-ergodic%20Volterra%20Cubic%20-In-press.pdf http://irep.iium.edu.my/73972/9/73972%20On%20Non-ergodic%20Volterra%20Cubic%20-In-press%20SCOPUS%20pdf.pdf |
| first_indexed |
2023-09-18T21:44:51Z |
| last_indexed |
2023-09-18T21:44:51Z |
| _version_ |
1777413381820514304 |