SHADOWING IS GENERIC ON VARIOUS ONE-DIMENSIONAL CONTINUA WITH A SPECIAL GEOMETRIC STRUCTURE

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F20%3AA2101X5R" target="_blank" >RIV/61988987:17610/20:A2101X5R - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1007%2Fs12220-019-00280-6" target="_blank" >https://link.springer.com/article/10.1007%2Fs12220-019-00280-6</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s12220-019-00280-6" target="_blank" >10.1007/s12220-019-00280-6</a>

Jazyk výsledku

angličtina

Název v původním jazyce

SHADOWING IS GENERIC ON VARIOUS ONE-DIMENSIONAL CONTINUA WITH A SPECIAL GEOMETRIC STRUCTURE

Popis výsledku v původním jazyce

In the paper we use a special geometric structure of selected one-dimensional continua to prove that some stronger versions of the shadowing property are generic (or at least dense) for continuous maps acting on these spaces.Specifically, we prove that: (i) the periodic TS -bi-shadowing prop- erty, where TS means some class of continuous methods, is generic as well as the s-limit shadowing property is dense in the space of all con- tinuous maps (and all continuous surjective maps) of any topological graph; (ii) the TS -bi-shadowing property is generic as well as the s-limit shadowing property is dense in the space of all continuous maps of any dendrite; (iii) the TS -bi-shadowing property is generic in the space of all continuous maps of chainable continuum that can by approximated by arcs from the inside.The results of the paper extend ones obtained over the last few deca- des by various authors (see, e.g., [11, 13, 14, 16, 17, 21, 27, 31]) for both homeomorphisms and continuous maps of compact manifolds, including (in particular) an interval and a circle, which are the simplest examples of one-dimensional continua. Moreover, from a technical point of view our considerations are a continuation of those carried out in the earlier work [16].

Název v anglickém jazyce

SHADOWING IS GENERIC ON VARIOUS ONE-DIMENSIONAL CONTINUA WITH A SPECIAL GEOMETRIC STRUCTURE

Popis výsledku anglicky

In the paper we use a special geometric structure of selected one-dimensional continua to prove that some stronger versions of the shadowing property are generic (or at least dense) for continuous maps acting on these spaces.Specifically, we prove that: (i) the periodic TS -bi-shadowing prop- erty, where TS means some class of continuous methods, is generic as well as the s-limit shadowing property is dense in the space of all con- tinuous maps (and all continuous surjective maps) of any topological graph; (ii) the TS -bi-shadowing property is generic as well as the s-limit shadowing property is dense in the space of all continuous maps of any dendrite; (iii) the TS -bi-shadowing property is generic in the space of all continuous maps of chainable continuum that can by approximated by arcs from the inside.The results of the paper extend ones obtained over the last few deca- des by various authors (see, e.g., [11, 13, 14, 16, 17, 21, 27, 31]) for both homeomorphisms and continuous maps of compact manifolds, including (in particular) an interval and a circle, which are the simplest examples of one-dimensional continua. Moreover, from a technical point of view our considerations are a continuation of those carried out in the earlier work [16].

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/LQ1602" target="_blank" >LQ1602: IT4Innovations excellence in science</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2020

Kód důvěrnosti údajů

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

Název periodika

Journal of Geometric Analysis

ISSN

1559-002X

e-ISSN

—

Svazek periodika

30

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

28

Strana od-do

1836-1864

Kód UT WoS článku

000523561300028

EID výsledku v databázi Scopus

2-s2.0-85074017528