The class of simple dynamics systems
Keywords:special points, non-ordinary points, critical points, order conjugacy, order isomorphism, labeled digraph, dynamically independent set
In this paper, we study the class of simple dynamical systems on 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.
K. Ali Akbar, Some results in linear, symbolic, and general topological dynamics, Ph. D. Thesis, University of Hyderabad (2010).
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
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
R. A. Holmgren, A first course in discrete dynamical systems, Springer-Verlag, NewYork, 1996. https://doi.org/10.1007/978-1-4419-8732-7
S. Patinkin, Transitivity implies period 6, preprint.
A. N. Sharkovskii, Coexistence of cycles of a continuous map of a line into itself, Ukr. Math. J. 16 (1964), 61-71.
J. Smital, A chaotic function with some extremal properties, Proc. Amer. Math. Soc. 87 (1983), 54-56. https://doi.org/10.2307/2044350
B. Sankara Rao, I. Subramania Pillai and V. Kannan, The set of dynamically special points, Aequationes Mathematicae 82, no. 1-2 (2011), 81-90. https://doi.org/10.1007/s00010-010-0066-6
How to Cite
This journal is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.