On variants of distributional chaos in dimension one

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F11%3A%230000301" target="_blank" >RIV/47813059:19610/11:#0000301 - isvavai.cz</a>

Výsledek na webu

<a href="http://www.tandfonline.com/doi/abs/10.1080/14689367.2011.588199" target="_blank" >http://www.tandfonline.com/doi/abs/10.1080/14689367.2011.588199</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1080/14689367.2011.588199" target="_blank" >10.1080/14689367.2011.588199</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On variants of distributional chaos in dimension one

Popis výsledku v původním jazyce

In their famous paper from 1994, B. Schwaizer and J. Smital, [B. Schwaizer and J. Smital, Measures of chaos and a spectral decomposition of dynamical systems on the interval, Trans. Amer. Math. Soc. 344 (1994), pp. 737-754] fully characterized topological entropy of interval maps in terms of distribution functions of distance between trajectories. Strictly speaking, they proved that a continuous map f :[0, 1]->[0, 1] has zero topological entropy if and only if for every x, y is an element of [0, 1] thefollowing limit exists: lim(n -> infinity) 1/n vertical bar{0 <= i < n : d (f(i)(x),f(i)(y)) < t}vertical bar for every real number t except at most countable set. While many partial efforts have been made in previous years, still there is no proof thatthe result of Schwaizer and Smital holds on every topological graph. Here we offer the proof of this fact, filling a gap existing in the literature of the topic.

Název v anglickém jazyce

On variants of distributional chaos in dimension one

Popis výsledku anglicky

In their famous paper from 1994, B. Schwaizer and J. Smital, [B. Schwaizer and J. Smital, Measures of chaos and a spectral decomposition of dynamical systems on the interval, Trans. Amer. Math. Soc. 344 (1994), pp. 737-754] fully characterized topological entropy of interval maps in terms of distribution functions of distance between trajectories. Strictly speaking, they proved that a continuous map f :[0, 1]->[0, 1] has zero topological entropy if and only if for every x, y is an element of [0, 1] thefollowing limit exists: lim(n -> infinity) 1/n vertical bar{0 <= i < n : d (f(i)(x),f(i)(y)) < t}vertical bar for every real number t except at most countable set. While many partial efforts have been made in previous years, still there is no proof thatthe result of Schwaizer and Smital holds on every topological graph. Here we offer the proof of this fact, filling a gap existing in the literature of the topic.

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

—

Návaznosti

Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2011

Kód důvěrnosti údajů

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

Název periodika

Dynamical Systems: An International Journal

ISSN

1468-9367

e-ISSN

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Svazek periodika

26

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

13

Strana od-do

273-285

Kód UT WoS článku

000299632100004

EID výsledku v databázi Scopus

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