A class of nonergodic lotka–volterra operators
On the basis of some numerical calculations,Ulam has conjectured that the ergodic theorem holds for any quadratic stochastic operator acting on a finite-dimensional simplex. However, Zakharevich showed that Ulam’s conjecture is false in general. Later, Ganikhodzhaev and Zanin generalized Zakharevich...
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| Format: | Article |
| Language: | English |
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Pleiades Publishing
2015
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| Online Access: | http://irep.iium.edu.my/45054/ http://irep.iium.edu.my/45054/1/Non_Ergodic_LV_Operator_---_MN.pdf |
| _version_ | 1848782716343943168 |
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| author | Saburov, Mansoor |
| author_facet | Saburov, Mansoor |
| author_sort | Saburov, Mansoor |
| building | IIUM Repository |
| collection | Online Access |
| description | On the basis of some numerical calculations,Ulam has conjectured that the ergodic theorem holds for any quadratic stochastic operator acting on a finite-dimensional simplex. However, Zakharevich showed that Ulam’s conjecture is false in general. Later, Ganikhodzhaev and Zanin generalized Zakharevich’s example to the class of quadratic stochastic Volterra operators acting on a 2D simplex. In this paper, we provide a class of nonergodic Lotka–Volterra operators which includes all previous operators used in this context. |
| first_indexed | 2025-11-14T16:09:53Z |
| format | Article |
| id | iium-45054 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T16:09:53Z |
| publishDate | 2015 |
| publisher | Pleiades Publishing |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-450542018-05-21T05:42:29Z http://irep.iium.edu.my/45054/ A class of nonergodic lotka–volterra operators Saburov, Mansoor QA Mathematics On the basis of some numerical calculations,Ulam has conjectured that the ergodic theorem holds for any quadratic stochastic operator acting on a finite-dimensional simplex. However, Zakharevich showed that Ulam’s conjecture is false in general. Later, Ganikhodzhaev and Zanin generalized Zakharevich’s example to the class of quadratic stochastic Volterra operators acting on a 2D simplex. In this paper, we provide a class of nonergodic Lotka–Volterra operators which includes all previous operators used in this context. Pleiades Publishing 2015 Article PeerReviewed application/pdf en http://irep.iium.edu.my/45054/1/Non_Ergodic_LV_Operator_---_MN.pdf Saburov, Mansoor (2015) A class of nonergodic lotka–volterra operators. Mathematical Notes, 97 (5). pp. 759-763. ISSN 0001-4346 http://link.springer.com/article/10.1134/S0001434615050107 |
| spellingShingle | QA Mathematics Saburov, Mansoor A class of nonergodic lotka–volterra operators |
| title | A class of nonergodic lotka–volterra operators |
| title_full | A class of nonergodic lotka–volterra operators |
| title_fullStr | A class of nonergodic lotka–volterra operators |
| title_full_unstemmed | A class of nonergodic lotka–volterra operators |
| title_short | A class of nonergodic lotka–volterra operators |
| title_sort | class of nonergodic lotka–volterra operators |
| topic | QA Mathematics |
| url | http://irep.iium.edu.my/45054/ http://irep.iium.edu.my/45054/ http://irep.iium.edu.my/45054/1/Non_Ergodic_LV_Operator_---_MN.pdf |