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Some strange properties of quadratic stochastic volterra operators

Saburov, Mansoor (2012) Some strange properties of quadratic stochastic volterra operators. World Applied Sciences Journal , 20. pp. 94-97. ISSN 1818-4952

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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.

Item Type: Article (Journal)
Uncontrolled Keywords: Regularity; Transitivity; Ergodic principle; Quadratic stochastic operator; Volterra operator.
Subjects: Q Science > QA Mathematics
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button): Kulliyyah of Science
Depositing User: Dr Mansoor Saburov
Date Deposited: 28 Dec 2012 08:25
Last Modified: 23 Apr 2013 10:55
URI: http://irep.iium.edu.my/id/eprint/27937

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