New chaotic planar attractors from smooth zero entropy interval maps

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F15%3AA1601BJC" target="_blank" >RIV/61988987:17610/15:A1601BJC - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
New chaotic planar attractors from smooth zero entropy interval maps
Original language description
We show that for every positive integer k there exists an interval map f:I?I such that (1) f is Li-Yorke chaotic, (2) the inverse limit space I_f=lim?{f,I} does not contain an indecomposable subcontinuum, (3) f is C^k-smooth, and (4) f is not C^(k+1)-smooth. We also show that there exists a C^?-smooth f that satisfies (1) and (2). This answers a recent question of Oprocha and the first author from (Proc. Am. Math. Soc. 143(8):3659-3670, 2015), where the result was proved for k=0. Our study builds on thework of Misiurewicz and Smítal of a family of zero entropy weakly unimodal maps. Some results on the structure of this continua are also mentioned. Finally, we prove that the chaotic attractors we construct are topologically distinct from the one presented by P. Oprocha and the first author.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/ED1.1.00%2F02.0070" target="_blank" >ED1.1.00/02.0070: IT4Innovations Centre of Excellence</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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