On Some Sets of Almost Continuous Functions which Locally Aproximate a Fixed Function
By: Anna Loranty and Ryszard J. Pawlak
References
- [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.
- [2] BLANCHARD, F.: Topological chaos: what this means? J. Difference Equ. Appl. 15 (2009), 23-46.
- [3] BLANCHARD, F.-HUANG, W.-SNOHA, L’: Topological size of scrambled set, Colloq. Math. 110 (2008), 293-361.
- [4] BLOCK, L. S.-COPPEL, W. A.: Dynamics in one Dimension. Lecture Notes in Math., Vol. 1513, Springer-Verlag, Berlin, 1992.
- [5] BOWEN, R.: Entropy for group endomorphisms and homogeneous spaces, Trans. Amer. Math. Soc. 153 (1971), 401-414; erratum 181 (1973), 509-510.
- [6] ČIKLOVÁ, M.: Dynamical systems generated by functions with connected Ggraphs, Real Anal. Exchange 30 (2004/2005), 617-638.
- [7] DINABURG, E. I.: The relation between topological entropy and metric entropy, Soviet Math. Doklady 11 (1970), 13-16.
- [8] JASTRZĘBSKI, J. M.-.JĘDRZEJEWSKI, J. M.-NATKANIEC, T.: On some subclass of Darboux functions, Fund. Math. 138 (1991), 165-173.
- [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.2014.34.4.799
- [10] KORCZAK-KUBIAK, E.-LORANTY, A.-PAWLAK, R. J.: On local problem, of entropy for functions from, Zahorski classes (to appear).
- [11] KWIETNIAK, D.-OPROCHA, P.: Topological entropy and chaos for maps induced on hyperspaces, Chaos Solitons Fractals 33 (2007), 76-86.
- [12] LI, J.-YE, X.: Recent development of chaos theory in topological dynamics, arXiv:1503.06425 [math.DS].
- [13] DE MELO, W.-VAN STRIEN, S.: One-Dimensional Dynamics. Springer-Verlag, Berlin, 1993.
- [14] NATKANIEC, T.: Almost continuity, Real Anal. Exchange 17 (1991/92), 462-520.
- [15] NATKANIEC, T.: Almost Continuity. Habilitation Thesis, Wyzsza Szkoła Pedagogiczna w Bydgoszczy, Bydgoszcz, 1992.
- [16] PAWLAK, R. J.: On points of extreme chaos for almost continuous functions, Tatra Mt. Math. Publ. 62 (2014).
- [17] PAWLAK, R. J.-LORANTY, A.-BA̡KOWSKA, A.: On the topological entropy of continuous and almost continuous functions, Topology Appl. 158 (2011), 2022-2033.
DOI: https://doi.org/10.1515/tmmp-2016-0009 | Journal eISSN: 1338-9750 (formerly 1210-3195) | Journal ISSN: 1210-3195
Language: English
Page range: 105 - 118
Submitted on: Nov 11, 2015
Published on: Aug 4, 2016
Published by: Slovak Academy of Sciences, Mathematical Institute
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year
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© 2016 Anna Loranty, Ryszard J. Pawlak, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.