Dynamické systémy generované funkcemi se souvislěm $G_delta$ grafem

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F05%3A%230000033" target="_blank" >RIV/47813059:19610/05:#0000033 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/47813059:19610/06:#0000092

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Dynamical systems generated by functions with connected $G_delta$ graphs

Popis výsledku v původním jazyce

In 2001, Cs" ornyei, O'Neil and Preiss proved that the composition of any two Darboux Baire-1 functions $[0,1]rightarrow[0,1]$ possesses a fixed point, solving a long-standing open problem. In 2004 Szuca proved that this result can be generalized to any $f$ in the class $mathcal J$ of functions $[0,1]rightarrow [0,1]$ with connected $G_delta$ graph. As a consequence, he proved that for such functions the Sharkovsky theorem is satisfied. As the main result of this paper we prove that similarly as for the continuous maps of the interval, any $f$ in $mathcal J$ has positive topological entropy if and only if it has a periodic point of period different from $2^n$, for any $ninmathbb N$. To do this we show that using the Bowen's approach it is possible to define topological entropy for discontinuous maps of a compact metric space with almost all standard properties. In particular, the variational principle is true, and consequently, topological e ntropy is supported by the set of re

Název v anglickém jazyce

Dynamical systems generated by functions with connected $G_delta$ graphs

Popis výsledku anglicky

In 2001, Cs" ornyei, O'Neil and Preiss proved that the composition of any two Darboux Baire-1 functions $[0,1]rightarrow[0,1]$ possesses a fixed point, solving a long-standing open problem. In 2004 Szuca proved that this result can be generalized to any $f$ in the class $mathcal J$ of functions $[0,1]rightarrow [0,1]$ with connected $G_delta$ graph. As a consequence, he proved that for such functions the Sharkovsky theorem is satisfied. As the main result of this paper we prove that similarly as for the continuous maps of the interval, any $f$ in $mathcal J$ has positive topological entropy if and only if it has a periodic point of period different from $2^n$, for any $ninmathbb N$. To do this we show that using the Bowen's approach it is possible to define topological entropy for discontinuous maps of a compact metric space with almost all standard properties. In particular, the variational principle is true, and consequently, topological e ntropy is supported by the set of re

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

<a href="/cs/project/GA201%2F03%2F1153" target="_blank" >GA201/03/1153: Dynamické systémy II.</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2005

Kód důvěrnosti údajů

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

Název periodika

Real Analysis Exchange

ISSN

0147-1937

e-ISSN

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Svazek periodika

30

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

21

Strana od-do

617-637

Kód UT WoS článku

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EID výsledku v databázi Scopus

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