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 2012
Subjects:	QA Mathematics
Online Access:	http://irep.iium.edu.my/27937/ http://irep.iium.edu.my/27937/ http://irep.iium.edu.my/27937/ http://irep.iium.edu.my/27937/1/Strange_Properties_V-QSO-WASJ.pdf

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spelling	iium-279372013-04-23T02:55:27Z http://irep.iium.edu.my/27937/ 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 2012 Article PeerReviewed application/pdf en http://irep.iium.edu.my/27937/1/Strange_Properties_V-QSO-WASJ.pdf Saburov, Mansoor (2012) Some strange properties of quadratic stochastic volterra operators. World Applied Sciences Journal , 20. pp. 94-97. ISSN 1818-4952 http://iosrjournals.org/ 10.5829/idosi.wasj.2012.20.mae.99929
repository_type	Digital Repository
institution_category	Local University
institution	International Islamic University Malaysia
building	IIUM Repository
collection	Online Access
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	2012
url	http://irep.iium.edu.my/27937/ http://irep.iium.edu.my/27937/ http://irep.iium.edu.my/27937/ http://irep.iium.edu.my/27937/1/Strange_Properties_V-QSO-WASJ.pdf
first_indexed	2023-09-18T20:41:23Z
last_indexed	2023-09-18T20:41:23Z
_version_	1777409388326158336

Some strange properties of quadratic stochastic volterra operators

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