Properties of topologically transitive maps on the real line

Kannan, V. ; Nagar, Anima ; Sesha Sai, S. P. (2001) Properties of topologically transitive maps on the real line Real Analysis Exchange, 27 (1). pp. 325-334. ISSN 0147-1937

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Official URL: http://msupress.msu.edu/journals/raex/index.php?Pa...

Abstract

We prove that every topologically transitive map f on the real line must satisfy the following properties: (1) The set C of critical points is unbounded. (2)The set f(C) of critical values is also unbounded. (3)Apart from the empty set and the whole set, there can be at most one open invariant set. (4)With a single possible exception, for every element x the backward orbit {y∈R:fn(y)=x for some n in N} is dense in R.

Item Type:Article
Source:Copyright of this article belongs to Michigan State University Press.
Keywords:Topologically Transitive Maps; Critical Points; Critical Values; Invariant Set
ID Code:96715
Deposited On:07 Jan 2013 04:41
Last Modified:07 Jan 2013 04:44

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