On Regular Solutions of the Generalized Dhombres Equation II

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F15%3A%230000503" target="_blank" >RIV/47813059:19610/15:#0000503 - isvavai.cz</a>
Result on the web
<a href="http://link.springer.com/article/10.1007%2Fs00025-015-0437-3" target="_blank" >http://link.springer.com/article/10.1007%2Fs00025-015-0437-3</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00025-015-0437-3" target="_blank" >10.1007/s00025-015-0437-3</a>

Result language
angličtina
Original language name
On Regular Solutions of the Generalized Dhombres Equation II
Original language description
We consider continuous solutions f: R+ -> R+ = (0, infinity) of the functional equation f(xf(x)) = phi(f(x)) where phi is a given continuous map from R+ to R+. A solution f is singular if there are a and b such that 0 < a <= b < infinity, f vertical bar((0,a)) > 1, f vertical bar([a,b]) equivalent to 1, and f vertical bar((b,infinity)) < 1; all other solutions are regular. It is known that the range R-f of a singular solution can contain, for every positive integer n, a periodic point of phi of period n. In this paper we show that the range of a regular solution f contains no periodic point of phi of period different from 1 and 2. Our proof is essentially based on a recent result that, for regular solutions phi vertical bar(Rf) has zero topological entropy. Since there are regular solutions containing periodic points of period 2 in the range, we get the best possible result.
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
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Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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