On Regular Solutions of the Generalized Dhombres Equation II

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

On Regular Solutions of the Generalized Dhombres Equation II

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

On Regular Solutions of the Generalized Dhombres Equation II

Popis výsledku anglicky

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.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2015

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Results in Mathematics

ISSN

1422-6383

e-ISSN

—

Svazek periodika

67

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

8

Strana od-do

521-528

Kód UT WoS článku

000354246500016

EID výsledku v databázi Scopus

2-s2.0-84930938078