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Title: $\mathcal F$-hypercyclic and disjoint $\mathcal F$-hypercyclic properties of binary relations over topological spaces (English)
Author: Kostić, Marko
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 145
Issue: 4
Year: 2020
Pages: 337-359
Summary lang: English
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Category: math
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Summary: We examine various types of $\mathcal F$-hypercyclic ($\mathcal F$-topologically transitive) and disjoint $\mathcal F$-hypercyclic (disjoint $\mathcal F$-topologically transitive) properties of binary relations over topological spaces. We pay special attention to finite structures like simple graphs, digraphs and tournaments, providing a great number of illustrative examples. (English)
Keyword: ${\mathcal F}$-hypercyclic binary relation
Keyword: ${\mathcal F}$-topologically transitive binary relation
Keyword: disjoint ${\mathcal F}$-hypercyclic binary relation
Keyword: disjoint ${\mathcal F}$-topologically transitive binary relation
Keyword: digraph
MSC: 47A16
MSC: 47B37
MSC: 47D06
idZBL: 07286017
idMR: MR4221838
DOI: 10.21136/MB.2019.0047-18
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Date available: 2020-11-18T09:55:16Z
Last updated: 2021-04-19
Stable URL: http://hdl.handle.net/10338.dmlcz/148427
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Reference: [1] Bayart, F., Grivaux, S.: Frequently hypercyclic operators.Trans. Am. Math. Soc. 358 (2006), 5083-5117. Zbl 1115.47005, MR 2231886, 10.1090/S0002-9947-06-04019-0
Reference: [2] Bayart, F., Matheron, É.: Dynamics of Linear Operators.Cambridge Tracts in Mathematics 179. Cambridge University Press, Cambridge (2009). Zbl 1187.47001, MR 2533318, 10.1017/CBO9780511581113
Reference: [3] Bès, J., Menet, Q., Peris, A., Puig, Y.: Strong transitivity properties for operators.Available at http://arxiv.org/pdf/arxiv:1703.03724. MR 3906215
Reference: [4] Bondy, J. A., Murty, U. S. R.: Graph Theory with Applications.American Elsevier Publishing, New York (1976). Zbl 1226.05083, MR 0411988, 10.1007/978-1-349-03521-2
Reference: [5] Bonilla, A., Grosse-Erdmann, K.-G.: Frequently hypercyclic operators and vectors.Ergodic Theory Dyn. Syst. 27 (2007), 383-404 erratum ibid. 29 2009 1993-1994. Zbl 1119.47011, MR 2308137, 10.1017/S014338570600085X
Reference: [6] Bonilla, A., Grosse-Erdmann, K.-G.: Upper frequent hypercyclicity and related notions.Rev. Mat. Complut. 31 (2018), 673-711. Zbl 06946767, MR 3847081, 10.1007/s13163-018-0260-y
Reference: [7] Chartrand, G., Lesniak, L.: Graphs and Digraphs.The Wadsworth & Brooks/Cole Mathematics Series. Wadsworth & Brooks/Cole Advanced Brooks & Software. VIII, Monterey (1986). Zbl 0666.05001, MR 0834583
Reference: [8] Chen, C.-C., Conejero, J. A., Kostić, M., Murillo-Arcila, M.: Dynamics of multivalued linear operators.Open Math. 15 (2017), 948-958. Zbl 06751707, MR 3674105, 10.1515/math-2017-0082
Reference: [9] Chen, C.-C., Conejero, J. A., Kostić, M., Murillo-Arcila, M.: Dynamics on binary relations over topological spaces.Symmetry 10 (2018), 12 pages. 10.3390/sym10060211
Reference: [10] Cvetković, D., Doobs, M., Sachs, H.: Spectra of Graphs: Theory and Applications.VEB Deutscher Verlag der Wissenschaften, Berlin (1980). Zbl 0458.05042, MR 0572262
Reference: [11] Cvetković, D., Rowlinson, P., Simić, S.: Eigenspaces of Graphs.Encyclopedia of Mathematics and Its Applications 66. Cambrige University Press, Cambridge (1997). Zbl 0878.05057, MR 1440854, 10.1017/CBO9781139086547
Reference: [12] Fürstenberg, H.: Recurrence in Ergodic Theory and Combinatorial Number Theory.M. B. Porter Lectures, Rice University, Department of Mathematics, 1978. Princeton University Press, Princeton (1981). Zbl 0459.28023, MR 0603625
Reference: [13] Grosse-Erdmann, K.-G., Manguillot, A. Peris: Linear Chaos.Universitext. Springer, Berlin (2011). Zbl 1246.47004, MR 2919812, 10.1007/978-1-4471-2170-1
Reference: [14] Kostić, M.: ${\mathcal F}$-hypercyclic linear operators on Fréchet spaces.. 10.13140/RG.2.2.26696.42245
Reference: [15] Kostić, M.: $\mathcal{F}$-hypercyclic extensions and disjoint ${\mathcal F}$-hypercyclic extensions of binary relations over topological spaces.Funct. Anal. Approx. Comput. 10 (2018), 41-52. Zbl 06902499, MR 3804275
Reference: [16] Mart'ı{n}ez-Avendaño, R. A.: Hypercyclicity of shifts on weighted {$L^p$} spaces of directed trees.J. Math. Anal. Appl. 446 (2017), 823-842. Zbl 1346.05032, MR 3554758, 10.1016/j.jmaa.2016.08.066
Reference: [17] Menet, Q.: Linear chaos and frequent hypercyclicity.Trans. Am. Math. Soc. 369 (2017), 4977-4994. Zbl 06705106, MR 3632557, 10.1090/tran/6808
Reference: [18] Moon, J. W.: Topics on Tournaments.Holt, Rinehart and Winston, New York (1968). Zbl 0191.22701, MR 0256919
Reference: [19] Moon, J. W., Pullman, N. J.: On the powers of tournament matrices.J. Comb. Theory 3 (1967), 1-9. Zbl 0166.00901, MR 0213264, 10.1016/S0021-9800(67)80009-7
Reference: [20] Namayanja, P.: Chaotic dynamics in a transport equation on a network.Discrete Contin. Dyn. Syst., Ser. B 23 (2018), 3415-3426. Zbl 06996836, MR 3848206, 10.3934/dcdsb.2018283
Reference: [21] Petrović, V.: Graph Theory.University of Novi Sad, Novi Sad (1998), Serbian.
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