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2004-2005 Convergence of a series whose terms are iterates of quadratic maps
Xiaorong Hou, Che Tat Ng, Weinian Zhang
Real Anal. Exchange 30(1): 277-288 (2004-2005).


The functional equation $k(p(x)) + k(x)= x, \ p(x)=x^2 +c$, was used to find quadratic invariant curves of a planar mapping. The continuity of its solutions $k$ on an interval is tied to its series representation through $\sum_{i=0}^{\infty}(p^{(2i)}(x)- p^{(2i+1)}(x))$, where the terms contain iterates of $p$. The intervals of convergence of the series deserve much attention. Because of the presence of iteration, such maximal intervals are sometimes difficult to determine. In this paper we show how numerical computations using Maple V5.1 and the use of discriminants and resultants may assist such development.


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Xiaorong Hou. Che Tat Ng. Weinian Zhang. "Convergence of a series whose terms are iterates of quadratic maps." Real Anal. Exchange 30 (1) 277 - 288, 2004-2005.


Published: 2004-2005
First available in Project Euclid: 27 July 2005

zbMATH: 1082.39017
MathSciNet: MR2127532

Primary: 40A30 , 65B110
Secondary: 37E05 , 39B22

Keywords: discriminant , Hadamard's gap condition , iteration , quadratic map , resultant , series

Rights: Copyright © 2004 Michigan State University Press

Vol.30 • No. 1 • 2004-2005
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