Singular Solutions of the Generalized Dhombres Functional Equation

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F14%3A%230000403" target="_blank" >RIV/47813059:19610/14:#0000403 - isvavai.cz</a>
Result on the web
<a href="http://link.springer.com/article/10.1007%2Fs00025-013-0345-3" target="_blank" >http://link.springer.com/article/10.1007%2Fs00025-013-0345-3</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00025-013-0345-3" target="_blank" >10.1007/s00025-013-0345-3</a>

Result language
angličtina
Original language name
Singular Solutions of the Generalized Dhombres Functional Equation
Original language description
We consider singular solutions of the functional equation f(xf(x)) =phi(f(x)) where phi is a given and f an unknown continuous map R+ -> R+. A solution f is regular if the sets R-f boolean AND (0,1]and R-f boolean AND [1,infinity), where R-f is the rangeof f, are phi-invariant; otherwise f is singular. We show that for singular solutions the associated dynamical system (R-f , phi vertical bar R-f) can have strange properties unknown for the regular solutions. In particular, we show that phi vertical bar R-f can have a periodic point of period 3 and hence can be chaotic in a strong sense. We also provide an effective method of construction of singular solutions.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—

Project
<a href="/en/project/GAP201%2F10%2F0887" target="_blank" >GAP201/10/0887: Discrete dynamical systems</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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