Sankara Rao, B. ; Subramania Pillai, I. ; Kannan, V. (2011) The set of dynamically special points Aequationes Mathematicae, 82 (1-2). pp. 81-90. ISSN 0001-9054
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Official URL: http://link.springer.com/article/10.1007%2Fs00010-...
Related URL: http://dx.doi.org/10.1007/s00010-010-0066-6
Abstract
We call a point “dynamically special” if it has a dynamical property, which no other point has. We prove that, for continuous self maps of the real line, all dynamically special points are in the closure of the union of the full orbits of periodic points, critical points and limits at infinity. We completely describe the set of dynamically special points of real polynomial functions. The following characterization for the set of special points is also obtained: A subset of R is the set of dynamically special points for some continuous self map of R if and only if it is closed.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Birkhauser-Verlag. |
| Keywords: | Primary 54H20; Secondary 37E05; Fixed Point; Periodic Point; Critical Point; Topological-Conjugacy |
| ID Code: | 96716 |
| Deposited On: | 29 Jan 2013 04:19 |
| Last Modified: | 29 Jan 2013 04:19 |
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