Some dynamic phenomena of iteration in R2

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Wang, Yongkui

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University of Guelph

Abstract

The present thesis investigates the iteration of a continuous mapping for which there exists a limit of the mapping as x and y approach the point (x0, y0), where x > x0, y > y0, on D = (x0, [infinity]) * (y0, [infinity]) in R 2. The author further explores how to determine a global stable domain (or convergent domain) in which the points tend to a quasi attracting fixed point (x0, y0) [4] on iteration of the mapping, subject to specified conditions. Two examples of iteration of two-dimensional mappings for which one of the coordinates is a rational function while the second coordinate is a polynomial function are discussed, as applications of the theorems derived in the thesis.

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Keywords

iteration, continuous mapping, limit, global stable domain, convergent domain, two-dimensional mappings, coordinates

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