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For graph maps, one scrambled pair implies Li-Yorke chaos
- Title
Title For graph maps, one scrambled pair implies Li-Yorke chaos Par.title Pre zobrazenia grafov, jedna chaotická dvojica implikuje Li-Yorkov chaos Author info Sylvie Ruette, Ľubomír Snoha Author Ruette Sylvie (50%)
Co-authors Snoha Ľubomír 1955- (50%) UMBFP10 - Katedra matematiky
Source document Proceedings of the American Mathematical Society. Vol. 142, no. 6 (2014), pp. 2087-2100. - Providence : American Mathematical Society, 2014 Keywords scrambled pair Li-Yorkov chaos - Li-Yorke chaos grafy - charts - graphs metrické priestory - metric spaces Language English Country United States of America systematics 51 Annotation It is known that, for interval and circle maps, the existence of a scrambled pair implies Li-Yorke chaos, in fact the existence of a Cantor scrambled set. We prove that the same result holds for graph maps. We further show that on compact countable metric spaces one scrambled pair implies the existence of an infinite scrambled set Public work category ADC No. of Archival Copy 31468 Repercussion category RAINES, Brian E. - UNDERWOOD, Tyler. Scrambled sets in shift spaces on a countable alphabet. In Proceedings of the American Mathematical Society. ISSN 0002-9939, 2016, vol. 144, no. 1, pp. 217-224.
ASKRI, Ghassen. Li-Yorke chaos for dendrite maps with zero topological entropy and omega-limit sets. In Discrete and continuous dynamical systems. ISSN 1078-0947, 2017, vol. 37, no. 6, pp. 2957-2976.
LI, Jian - OPROCHA, Piotr - YANG, Yini - ZENG, Tiaoying. On dynamics of graph maps with zero topological entropy. In Nonlinearity. ISSN 0951-7715, 2017, vol. 30, no. 12, pp. 4260-4276.
EL ABDALAOUI, El Houcein - ASKRI, Ghassen - MARZOUGUI, Habib. Mobius disjointness conjecture for local dendrite maps. In Nonlinearity. ISSN 0951-7715, 2019, vol. 32, no. 1, pp. 285-300.
KOSTIĆ, Marko. Chaos for linear operators and abstract differential equations. [Hauppauge] : Nova science publishers, 2020. 338 p. ISBN 978-153616896-9.
LI, Jian - LIANG, Xianjuan - OPROCHA, Piotr. Graph maps with zero topological entropy and sequence entropy pairs. In Proceedings of the American mathematical society. ISSN 0002-9939, 2021, vol. 149, no. 11, pp. 4757-4770.
FORYS-KRAWIEC, Magdalena - HANTAKOVA, Jana - OPROCHA, Piotr. On the structure of α-limit sets of backward trajectories for graph maps. In Discrete and continuous dynamical systems. ISSN 1078-0947, 2022, vol. 42, no. 3, pp. 1435-1463.
ABDELLI, Hafedh - NAGHMOUCHI, Issam - REZGUI, Houssem Eddine. Local dendrite maps without periodic points. In Topology and its applications. ISSN 0166-8641, 2022, vol. 305, art. no. 107901, pp. 1-14.
LI, Jian - OPROCHA, Piotr - ZHANG, Guohua. Quasi-graphs, zero entropy and measures with discrete spectrum. In Nonlinearity. ISSN 0951-7715, 2022, vol. 35, no. 3, pp. 1360-1379.
ABDELLI, Hafedh - MARZOUGUI, Habib - MCHAALIA, Amira. Recurrence and nonwandering sets of local dendrite maps. In Journal of difference equations and applications. ISSN 1023-6198, 2023, vol. 29, no. 9-12. DOI: https://doi.org/10.1080/10236198.2022.2038143
JELIC, Domagoj - OPROCHA, Piotr. On recurrence and entropy in the hyperspace of continua in dimension one. In Fundamenta mathematicae. ISSN 0016-2736, 2023, vol. 263, no. 1, pp. 23-50. DOI: https://doi.org/10.4064/fm235-4-2023[23]
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MAI, Jiehua - ZHOU, Lei - SUN, Taixiang. Cardinalities of scrambled sets and positive scrambled sets. In Topology and its applications. ISSN 0166-8641, 2024, vol. 342, art. no. 108781. pp. 1-15. DOI: https://doi.org/10.1016/j.topol.2023.108781
Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ References PERIODIKÁ-Súborný záznam periodika 
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Minimal spaces with cyclic group of homeomorphismsAuthor infoTomasz Downarowicz, Ľubomír Snoha, Dariusz TywoniukAuthorCo-authorsSource documentJournal of Dynamics and Differential Equations. Vol. 29, no. 1 (2017), pp. 243-257. - New York : Springer, 2017Keywords
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