Akbar, Kamaludheen Ali The class of simple dynamics systems. (English) Zbl 1452.37021 Appl. Gen. Topol. 21, No. 2, 215-233 (2020). Summary: In this paper, we study the class of simple dynamical systems on \(\mathbb{R}\) induced by continuous maps having finitely many non-ordinary points. We characterize this class using labeled digraphs and dynamically independent sets. In fact, we classify dynamical systems up to their number of non-ordinary points. In particular, we discuss about the class of continuous maps having unique non-ordinary point, and the class of continuous maps having exactly two non-ordinary points. Cited in 1 Document MSC: 37C15 Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems 37C25 Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics 26A21 Classification of real functions; Baire classification of sets and functions 26A48 Monotonic functions, generalizations Keywords:special points; non-ordinary points; critical points; order conjugacy; order isomorphism; labeled digraph; dynamically independent set PDFBibTeX XMLCite \textit{K. A. Akbar}, Appl. Gen. Topol. 21, No. 2, 215--233 (2020; Zbl 1452.37021) Full Text: Link References: [1] K. Ali Akbar, Some results in linear, symbolic, and general topological dynamics, Ph. D. Thesis, University of Hyderabad (2010). [3] K. Ali Akbar, V. Kannan and I. Subramania Pillai, Simple dynamical systems, Applied General Topology 2, no. 2 (2019), 307-324. https://doi.org/10.4995/agt.2019.7910 · Zbl 1426.37022 [5] A. Brown and C. Pearcy, An introduction to analysis (Graduate Texts in Mathematics), Springer-Verlag, New York, 1995. https://doi.org/10.1007/978-1-4612-0787-0 · Zbl 0820.00003 [7] R. A. Holmgren, A first course in discrete dynamical systems, Springer-Verlag, NewYork, 1996. https://doi.org/10.1007/978-1-4419-8732-7 · Zbl 0855.58042 [9] S. Patinkin, Transitivity implies period 6, preprint. [11] A. N. Sharkovskii, Coexistence of cycles of a continuous map of a line into itself, Ukr. Math. J. 16 (1964), 61-71. · Zbl 0122.17504 [13] J. Smital, A chaotic function with some extremal properties, Proc. Amer. Math. Soc. 87 (1983), 54-56. https://doi.org/10.2307/2044350 · Zbl 0555.26003 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.