Imperial College London
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DrPaulVerschueren

Faculty of Natural Sciences, Department of Mathematics

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p.verschueren

 
 
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Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Verschueren:2014:10.1080/10236198.2014.899357,
author = {Verschueren, P and Mestel, BD},
doi = {10.1080/10236198.2014.899357},
journal = {Journal of Difference Equations and Applications},
pages = {1152--1168},
title = {Fixed points of Composition Sum Operators},
url = {http://dx.doi.org/10.1080/10236198.2014.899357},
volume = {20},
year = {2014}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - In the renormalisation analysis of critical phenomena in quasi-periodicsystems, a fundamental role is often played by fixed points of functionalrecurrences of the form \begin{equation} f_{n}(x) = \sum_{i=1}^\ell a_i(x)f_{n_i} (\alpha_i(x)) \,, \end{equation} where the $\alpha_i$, $a_i$ are knownfunctions and the $n_i$ are given and satisfy $n-2 \le n_i \le n-1 $. Wedevelop a general theory of fixed points of ``Composition Sum Operators''derived from such recurrences, and apply it to test for fixed points in keyclasses of complex analytic functions with singularities. Finally wedemonstrate the construction of the full space of fixed points of one importantclass, for the much studied operator \begin{equation} Mf(x) = f(-\omega x) +f(\omega^2 x + \omega)\,, \quad \omega = (\sqrt{5}-1)/2\,. \end{equation} Theconstruction reveals previously unknown solutions.
AU  - Verschueren,P
AU  - Mestel,BD
DO  - 10.1080/10236198.2014.899357
EP  - 1168
PY  - 2014///
SN  - 1023-6198
SP  - 1152
TI  - Fixed points of Composition Sum Operators
T2  - Journal of Difference Equations and Applications
UR  - http://dx.doi.org/10.1080/10236198.2014.899357
UR  - http://hdl.handle.net/10044/1/48275
VL  - 20
ER  -
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