Dynamics of Darboux functions

[1] ALSED`A, L.-LLIBRE, J.-MISIUREWICZ M.: Combinatorial Dynamics and Entropy in Dimension One, in: Adv. Ser. Nonlinear Dynam., Vol. 5, World Scientific, Singapore, 1993.10.1142/1980Search in Google Scholar

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

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

[4] BRUCKNER, A. M.: Differentation of Real Functions, in: Lecture Notes in Math., Vol. 659, Springer-Verlag, Berlin, 1978.10.1007/BFb0069821Search in Google Scholar

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

[6] CRANNELL, A.-MARTELLI, M.: Dynamics of quasicontinuous systems, J. Difference Equ. Appl. 6 (2000), 351-361.10.1080/10236190008808234Search in Google Scholar

[7] DEVANEY, R. L.: Chaotic Dynamical Systems (2nd ed.), Addison-Wesley Publ. Comp., Redwood City, CA, 1989.Search in Google Scholar

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

[9] ENGELKING, R.: General Topology, PWN-Polish Scientific Publishers, Warszawa, 1977.Search in Google Scholar

[10] KELLUM, K. L.: Iterates of almost continuous functions and Sharkovskii’s theorem, Real Anal. Exchange 14 (1988-1989), 420-422.10.2307/44151956Search in Google Scholar

[11] PAWLAK, H.-PAWLAK, R.: Transitivity, dense orbits and some topologies finer than the natural topology of the unit interval, Tatra Mt. Math. Publ. 35 (2007), 1-12.Search in Google Scholar

[12] PAWLAK, R. J.: On Sharkovsky’s property of Darboux functions, Tatra Mt. Math. Publ. 42 (2009) 95-105.Search in Google Scholar

[13] PAWLAK, R. J.: On the entropy of Darboux functions, Colloq. Math. (to appear).Search in Google Scholar

[14] PERIS, A.: Transitivity, dense orbit and discontinuous functions, Bull. Belg. Math. Soc. 6 (1999), 391-394.Search in Google Scholar

[15] STALLINGS, J.: Fixed point theorem for a connectivity maps, Fund. Math. 47 (1959), 249-263.10.4064/fm-47-3-249-263Search in Google Scholar

[16] SZUCA, P.: Punkty Sta_le Odwzorowa´n Typu Darboux. Doctoral Thesis, Gda´nsk, 2003. (In Polish)Search in Google Scholar

[17] SZUCA, P.: Sharkovski˘ı’s theorem holds for some discontinuous functions, Fund. Math. 179 (2003), 27-41.10.4064/fm179-1-3Search in Google Scholar

[18] VALLEKOOP, M.-BERGLUND, R.: On intervals, transitivity chaos, Amer. Math. Monthly 101 (1994), 353-353.Search in Google Scholar