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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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Main Author: Saburov, Mansoor
Format: Article
Language:English
Published: IDOSI Publication 2013
Subjects:
QA Mathematics
Online Access:http://irep.iium.edu.my/29660/1/saburov.pdf
http://irep.iium.edu.my/29660/
http://www.idosi.org/wasj/WASJ21(mae)13/17.pdf
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spelling my.iium.irep.296602013-04-23T02:56:04Z http://irep.iium.edu.my/29660/ 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 2013-05-01 Article REM application/pdf en http://irep.iium.edu.my/29660/1/saburov.pdf Saburov, Mansoor (2013) Some strange properties of quadratic stochastic volterra operators. World Applied Sciences Journal (21). pp. 94-97. ISSN 1818-4952 http://www.idosi.org/wasj/WASJ21(mae)13/17.pdf 10.5829/idosi.wasj.2013.21.mae.99929
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
topic QA Mathematics
spellingShingle QA Mathematics
Saburov, Mansoor
Some strange properties of quadratic stochastic volterra operators
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.
format Article
author Saburov, Mansoor
author_facet Saburov, Mansoor
author_sort Saburov, Mansoor
title Some strange properties of quadratic stochastic volterra operators
title_short 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_sort some strange properties of quadratic stochastic volterra operators
publisher IDOSI Publication
publishDate 2013
url http://irep.iium.edu.my/29660/1/saburov.pdf
http://irep.iium.edu.my/29660/
http://www.idosi.org/wasj/WASJ21(mae)13/17.pdf
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score 13.211869

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