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For graph maps, one scrambled pair implies Li-Yorke chaos
Názov For graph maps, one scrambled pair implies Li-Yorke chaos Súbež.n. Pre zobrazenia grafov, jedna chaotická dvojica implikuje Li-Yorkov chaos Aut.údaje Sylvie Ruette, Ľubomír Snoha Autor Ruette Sylvie (50%)
Spoluautori Snoha Ľubomír 1955- (50%) UMBFP10 - Katedra matematiky
Zdroj.dok. Proceedings of the American Mathematical Society. Vol. 142, no. 6 (2014), pp. 2087-2100. - Providence : American Mathematical Society, 2014 Kľúč.slová scrambled pair Li-Yorkov chaos - Li-Yorke chaos grafy - charts - graphs metrické priestory - metric spaces Jazyk dok. angličtina Krajina Spojené štáty Systematika 51 Anotácia 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 Kategória publikačnej činnosti ADC Číslo archívnej kópie 31468 Kategória ohlasu 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.
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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
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