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

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
SHADOWING IS GENERIC ON VARIOUS ONE-DIMENSIONAL CONTINUA WITH A SPECIAL GEOMETRIC STRUCTURE
Original language description
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].
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/LQ1602" target="_blank" >LQ1602: IT4Innovations excellence in science</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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