On Some Sets of Almost Continuous Functions which Locally Aproximate a Fixed Function

[1] ALSEDÁ, L.-LLIBRE, J.-MISIUREWICZ, M.: Combinatorial Dynamics and Entropy in Dimension One (2nd ed.), in: Adv. Ser. Nonlinear Dynam., Vol. 5, World Sci., Singapore, 2000.Search in Google Scholar

[2] BLANCHARD, F.: Topological chaos: what this means? J. Difference Equ. Appl. 15 (2009), 23-46.10.1080/10236190802385355Search in Google Scholar

[3] BLANCHARD, F.-HUANG, W.-SNOHA, L’: Topological size of scrambled set, Colloq. Math. 110 (2008), 293-361.10.4064/cm110-2-3Search in Google Scholar

[4] BLOCK, L. S.-COPPEL, W. A.: Dynamics in one Dimension. Lecture Notes in Math., Vol. 1513, Springer-Verlag, Berlin, 1992.Search in Google Scholar

[5] BOWEN, R.: Entropy for group endomorphisms and homogeneous spaces, Trans. Amer. Math. Soc. 153 (1971), 401-414; erratum 181 (1973), 509-510.Search in Google Scholar

[6] ČIKLOVÁ, M.: Dynamical systems generated by functions with connected G_δ graphs, Real Anal. Exchange 30 (2004/2005), 617-638.10.14321/realanalexch.30.2.0617Search in Google Scholar

[7] DINABURG, E. I.: The relation between topological entropy and metric entropy, Soviet Math. Doklady 11 (1970), 13-16.Search in Google Scholar

[8] JASTRZĘBSKI, J. M.-.JĘDRZEJEWSKI, J. M.-NATKANIEC, T.: On some subclass of Darboux functions, Fund. Math. 138 (1991), 165-173.10.4064/fm-138-3-165-173Search in Google Scholar

[9] KORCZAK-KUBIAK, E.-LORANTY, A.-PAWLAK, R. J.: On oo-entropy points in real analysis, Opuscula Math. 34 (2014), 799-812, http://dx.doi.org/10.7494/OpMath.2014.34.4.79910.7494/OpMath.2014.34.4.799Search in Google Scholar

[10] KORCZAK-KUBIAK, E.-LORANTY, A.-PAWLAK, R. J.: On local problem, of entropy for functions from, Zahorski classes (to appear).Search in Google Scholar

[11] KWIETNIAK, D.-OPROCHA, P.: Topological entropy and chaos for maps induced on hyperspaces, Chaos Solitons Fractals 33 (2007), 76-86.10.1016/j.chaos.2005.12.033Search in Google Scholar

[12] LI, J.-YE, X.: Recent development of chaos theory in topological dynamics, arXiv:1503.06425 [math.DS].Search in Google Scholar

[13] DE MELO, W.-VAN STRIEN, S.: One-Dimensional Dynamics. Springer-Verlag, Berlin, 1993.10.1007/978-3-642-78043-1Search in Google Scholar

[14] NATKANIEC, T.: Almost continuity, Real Anal. Exchange 17 (1991/92), 462-520.10.2307/44153745Search in Google Scholar

[15] NATKANIEC, T.: Almost Continuity. Habilitation Thesis, Wyzsza Szkoła Pedagogiczna w Bydgoszczy, Bydgoszcz, 1992.Search in Google Scholar

[16] PAWLAK, R. J.: On points of extreme chaos for almost continuous functions, Tatra Mt. Math. Publ. 62 (2014).10.1515/tmmp-2015-0012Search in Google Scholar

[17] PAWLAK, R. J.-LORANTY, A.-BA̡KOWSKA, A.: On the topological entropy of continuous and almost continuous functions, Topology Appl. 158 (2011), 2022-2033. 10.1016/j.topol.2011.06.049Search in Google Scholar