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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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Main Authors:	Mukhamedov, Farrukh, Pah, Chin Hee, Rosli, Azizi
Format:	Article
Language:	English English English
Published:	Springer 2019
Subjects:	QA Mathematics
Online Access:	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 http://irep.iium.edu.my/73972/ https://link.springer.com/article/10.1007/s12346-019-00334-8
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spelling	my.iium.irep.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
institution	Universiti Islam Antarabangsa Malaysia
building	IIUM Library
collection	Institutional Repository
continent	Asia
country	Malaysia
content_provider	International Islamic University Malaysia
content_source	IIUM Repository (IREP)
url_provider	http://irep.iium.edu.my/
language	English 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/73972/1/73972_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 http://irep.iium.edu.my/73972/ https://link.springer.com/article/10.1007/s12346-019-00334-8
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score	13.211869

On non-ergodic volterra cubic stochastic operators

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