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@article{CHFMJ_2019_4_1_a3, author = {M. Kosti\'c}, title = {Distributional chaos and {Li~---} {Yorke} chaos in metric spaces}, journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal}, pages = {42--58}, publisher = {mathdoc}, volume = {4}, number = {1}, year = {2019}, language = {en}, url = {http://geodesic.mathdoc.fr/item/CHFMJ_2019_4_1_a3/} }
M. Kostić. Distributional chaos and Li~--- Yorke chaos in metric spaces. Čelâbinskij fiziko-matematičeskij žurnal, Tome 4 (2019) no. 1, pp. 42-58. http://geodesic.mathdoc.fr/item/CHFMJ_2019_4_1_a3/
[1] Bayart F., Matheron E., Dynamics of Linear Operators, Cambridge University Press, Cambridge, 2009, 337 pp. | MR | Zbl
[2] Grosse-Erdmann K.-G., Peris A., Linear Chaos, Springer-Verlag, London, 2011, 388 pp. | MR | Zbl
[3] Conejero J.A., Chen C.-C., Kostić M., Murillo-Arcila M., “Dynamics of multivalued linear operators”, Open Mathematics, 15 (2017), 948–958 | MR | Zbl
[4] Abakumov E., Boudabbous M., Mnif M., “On hypercyclicity of linear relations”, Results in Mathematics, 73:137 (2018), 1–17 | MR
[5] Conejero J.A., Chen C.-C., Kostić M., Murillo-Arcila M., “Dynamics on binary relations over topological spaces”, Symmetry, 10:211 (2018), 1–12
[6] Kostić M., “${\mathcal F}$-hypercyclic extensions and disjoint ${\mathcal F}$-hypercyclic extensions of binary relations over topological spaces”, Functional Analysis, Approximation and Computation, 10 (2018), 41–52 | MR | Zbl
[7] Schweizer B., Smítal J., “Measures of chaos and a spectral decomposition of dynamical systems on the interval”, Transactions of the American Mathematical Society, 344 (1994), 737–754 | DOI | MR | Zbl
[8] Duan J., Fu X.-C., Liu P.-D., Manning A., “A linear chaotic quantum harmonic oscillator”, Applied Mathematics Letters, 12 (1999), 15–19 | DOI | MR | Zbl
[9] Oprocha P., “A quantum harmonic oscillator and strong chaos”, Journal of Physics. A, 39 (2006), 14559–14565 | DOI | MR | Zbl
[10] Bernardes Jr. N.C., Bonilla A., Müler V., Peris A., “Distributional chaos for linear operators”, Journal of Functional Analysis, 265:1 (2013), 2143–2163 | DOI | MR | Zbl
[11] Conejero J.A., Kostić M., Miana P.J., Murillo-Arcila M., “Distributionally chaotic families of operators on Fréchet spaces”, Communications of Pure and Applied Analysis, 15 (2016), 1915–1939 | DOI | MR | Zbl
[12] Li T.Y., Yorke J.A., “Period three implies chaos.”, The American Mathematics Monthly, 2 (1975), 985–992 | MR
[13] Bermúdez T., Bonilla A,, Martinez-Gimenez F., Peris A., “Li — Yorke and distributionally chaotic operators”, Journal of Mathematical Analysis and Applications, 373 (2011), 83–93 | DOI | MR | Zbl
[14] Bernardes Jr. N.C., Bonilla A., Müler V., Peris A., “Li — Yorke chaos in linear dynamics”, Ergodic Theory and Dynamical Systems, 35 (2015), 1723–1745 | DOI | MR | Zbl
[15] Akin E., Kolyada S., “Li — Yorke sensitivity”, Nonlinearity, 16 (2003), 1421–1433 | DOI | MR | Zbl
[16] Blanchard F., Glasner E., Kolyada S., Maass A., “On Li — Yorke pairs”, Journal für die reine und angewandte Mathematik, 547 (2002), 51–68 | MR | Zbl
[17] Fu H.M., Xiong J.C., Wang H.Y., “The hierarchy of distributional chaos”, International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 25:1 (2015), 1550001-1–1550001-10 | DOI | MR | Zbl
[18] Huang W., Ye X., “Devaney's chaos or 2-scattering implies Li — Yorke chaos”, Topology and its Applications, 117 (2002), 259–272 | DOI | MR | Zbl
[19] Kostić M., “Li — Yorke chaotic properties of abstract differential equations of first order”, Applied Mathematics Computing Sciences, 1 (2016), 15–26
[20] Luo L., Hou B., “Some remarks on distributional chaos for bounded linear operators”, Turkish Journal of Mathematics, 39 (2015), 251–258 | DOI | MR | Zbl
[21] Oprocha P., “Distributional chaos revisited”, Transactions of the American Mathematical Society, 361 (2009), 4901–4925 | DOI | MR | Zbl
[22] Tan F., Fu H.M., “On distributional $n-$chaos”, Acta Mathematica Scientia. Series B. English Edition, 34:5 (2014), 1473–1480 | DOI | MR | Zbl
[23] Bernardes Jr. N.C., Bonilla A., Peris A., Wu X., “Distributional chaos for operators on Banach spaces”, Journal of Mathematical Analysis and Applications, 459 (2018), 797–821 | DOI | MR | Zbl
[24] Cross R., Multivalued Linear Operators, Taylor Francis Inc., New York, 1998, 352 pp. | MR
[25] Favini A., Yagi A., Degenerate Differential Equations in Banach Spaces, Marcel Dekker Inc., New York, Basel, Hong Kong, 1998, 314 pp. | MR
[26] Sviridyuk G.A., Fedorov V.E., Linear Sobolev Type Equations and Degenerate Semigroups of Operators, VSP, Utrecht, Boston, 2003, 216 pp. | MR | Zbl
[27] Kostić M., Generalized Semigroups and Cosine Functions, Mathematical Institute SANU, Belgrade, 2011, 355 pp. | MR | Zbl
[28] Kostić M., Abstract Volterra Integro-Differential Equations, CRC Press, Boca Raton, Fl., 2015, 484 pp. | MR | Zbl