On regular solutions of the generalized Dhombres equation

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F15%3A%230000465" target="_blank" >RIV/47813059:19610/15:#0000465 - isvavai.cz</a>

Result on the web

<a href="http://link.springer.com/article/10.1007%2Fs00010-014-0272-8" target="_blank" >http://link.springer.com/article/10.1007%2Fs00010-014-0272-8</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00010-014-0272-8" target="_blank" >10.1007/s00010-014-0272-8</a>

Result language

angličtina

Original language name

On regular solutions of the generalized Dhombres equation

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 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.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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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

2015

Confidentiality

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

Name of the periodical

Aequationes mathematicae

ISSN

0001-9054

e-ISSN

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Volume of the periodical

89

Issue of the periodical within the volume

1

Country of publishing house

CH - SWITZERLAND

Number of pages

5

Pages from-to

57-61

UT code for WoS article

000351225000006

EID of the result in the Scopus database

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