1. For graph maps, one scrambled pair implies Li-Yorke chaos
| 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] NAGHMOUCHI, Issam - REZGUI, Houssem Eddine. One-dimensional systems without periodic points. In International journal of bifurcation and chaos. ISSN 0218-1274, 2023, vol. 33, no. 13, pp. 1-19. DOI: https://doi.org/10.1142/S0218127423501511 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 |