On regular solutions of the generalized Dhombres equation

Kód výsledku v IS VaVaI

RIV/47813059:19610/15:#0000465 - isvavai.cz

Výsledek na webu

http://link.springer.com/article/10.1007%2Fs00010-014-0272-8

DOI - Digital Object Identifier

10.1007/s00010-014-0272-8

Jazyk výsledku

angličtina

Název v původním jazyce

On regular solutions of the generalized Dhombres equation

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 R+ -> R+. A solution f is singular if there are 0 < a <= b < infinity such that f vertical bar((0, a)) > 1,f vertical bar([a, b]) = 1, and f vertical bar((b, infinity)) < 1; other solutions are regular. It is known that the range R-f of a singular solution can contain periodic orbits of phi of all periods. In this paper we show that the range of a regular solution f contains no periodic point of phi of period different from 2(n), n is an element of N so that phi vertical bar R-f has zero topological entropy. It follows, that the regular solutions are just the solutions f satisfying one of the conditions: (i)R-f subset of (0, 1], (ii) R-f subset of [1, infinity), (iii) there are 0 < a <= b < infinity such that f(vertical bar(0, a)) < 1, f(vertical bar[a, b] equivalent to) 1, and f(vertical bar(b,infinity)) > 1.

Název v anglickém jazyce

On regular solutions of the generalized Dhombres equation

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 R+ -> R+. A solution f is singular if there are 0 < a <= b < infinity such that f vertical bar((0, a)) > 1,f vertical bar([a, b]) = 1, and f vertical bar((b, infinity)) < 1; other solutions are regular. It is known that the range R-f of a singular solution can contain periodic orbits of phi of all periods. In this paper we show that the range of a regular solution f contains no periodic point of phi of period different from 2(n), n is an element of N so that phi vertical bar R-f has zero topological entropy. It follows, that the regular solutions are just the solutions f satisfying one of the conditions: (i)R-f subset of (0, 1], (ii) R-f subset of [1, infinity), (iii) there are 0 < a <= b < infinity such that f(vertical bar(0, a)) < 1, f(vertical bar[a, b] equivalent to) 1, and f(vertical bar(b,infinity)) > 1.

Druh

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

CEP obor

BA - Obecná matematika

OECD FORD obor

—

Projekt

GAP201/10/0887: Diskrétní dynamické systémy

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

Aequationes mathematicae

ISSN

0001-9054

e-ISSN

—

Svazek periodika

89

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

5

Strana od-do

57-61

Kód UT WoS článku

000351225000006

EID výsledku v databázi Scopus

—