New chaotic planar attractors from smooth zero entropy interval maps
Result 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.
Keywords
weakly unimodal maparc-likeLi-Yorke chaoticindecomposable continuumzero topological entropy
The result's identifiers
Result code in IS VaVaI
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
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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Classification
Type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Advances in Difference Equations
ISSN
1687-1847
e-ISSN
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Volume of the periodical
2015
Issue of the periodical within the volume
1
Country of publishing house
US - UNITED STATES
Number of pages
11
Pages from-to
1-11
UT code for WoS article
000358525200001
EID of the result in the Scopus database
2-s2.0-84938832970
Basic information
Result type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP
BA - General mathematics
Year of implementation
2015