On conjugacy of natural extensions of one-dimensional maps

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F23%3AA2402CEF" target="_blank" >RIV/61988987:17610/23:A2402CEF - isvavai.cz</a>
Result on the web
<a href="https://www.doi.org/10.1017/etds.2022.62" target="_blank" >https://www.doi.org/10.1017/etds.2022.62</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1017/etds.2022.62" target="_blank" >10.1017/etds.2022.62</a>

Result language
angličtina
Original language name
On conjugacy of natural extensions of one-dimensional maps
Original language description
We prove that for any nondegenerate dendrite D there exist topologically mixing maps F:D→D and f:[0,1]→[0,1], such that the natural extensions (aka shift homeomorphisms) σF and σf are conjugate, and consequently the corresponding inverse limits are homeomorphic. Moreover, the map f does not depend on the dendrite D, and can be selected so that the inverse limit lim←−−(D,F) is homeomorphic to the pseudo-arc. The result extends to any finite number of dendrites. Our work is motivated by, but independent of, the recent result of the first and third author on conjugation of Lozi and Hénon maps to natural extensions of dendrite maps.
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
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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