On the spectrum of dynamical systems on trees

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F17%3AA0000018" target="_blank" >RIV/47813059:19610/17:A0000018 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S0166864117301773" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0166864117301773</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.topol.2017.03.007" target="_blank" >10.1016/j.topol.2017.03.007</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On the spectrum of dynamical systems on trees

Popis výsledku v původním jazyce

In their paper, Schweizer and Smital (1994) [10] introduced the notions of distributional chaos for continuous maps of the interval, spectrum and weak spectrum of a dynamical system. Among other things, they have proved that in the case of continuous interval maps, both the spectrum and the weak spectrum are finite and generated by points from the basic sets. Here we generalize the mentioned results for the case of continuous maps of a finite tree. While the results are similar, the original argument is not applicable directly and needs essential modifications. In particular, it was necessary to resolve the problem of intersection of basic sets, which was a crucial point. An example of one-dimensional dynamical system with an infinite spectrum is presented.

Název v anglickém jazyce

On the spectrum of dynamical systems on trees

Popis výsledku anglicky

In their paper, Schweizer and Smital (1994) [10] introduced the notions of distributional chaos for continuous maps of the interval, spectrum and weak spectrum of a dynamical system. Among other things, they have proved that in the case of continuous interval maps, both the spectrum and the weak spectrum are finite and generated by points from the basic sets. Here we generalize the mentioned results for the case of continuous maps of a finite tree. While the results are similar, the original argument is not applicable directly and needs essential modifications. In particular, it was necessary to resolve the problem of intersection of basic sets, which was a crucial point. An example of one-dimensional dynamical system with an infinite spectrum is presented.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2017

Kód důvěrnosti údajů

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

Název periodika

Topology and its Applications

ISSN

0166-8641

e-ISSN

1879-3207

Svazek periodika

222

Číslo periodika v rámci svazku

May

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

11

Strana od-do

227-237

Kód UT WoS článku

000399508200016

EID výsledku v databázi Scopus

2-s2.0-85015447439