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2001/2002 Properties of Topologically Transitive Maps on the Real Line
Anima Nagar
Real Anal. Exchange 27(1): 325-334 (2001/2002).


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 $\{y\in {\mathbb R} : f^n(y) = x$ for some $n$ in ${\mathbb N}\}$ is dense in ${\mathbb R}$.


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Anima Nagar. "Properties of Topologically Transitive Maps on the Real Line." Real Anal. Exchange 27 (1) 325 - 334, 2001/2002.


Published: 2001/2002
First available in Project Euclid: 6 June 2008

zbMATH: 1015.37030
MathSciNet: MR1887863

Primary: 54H20‎

Keywords: critical points , critical values , invariant set , Topologically transitive maps

Rights: Copyright © 2001 Michigan State University Press

Vol.27 • No. 1 • 2001/2002
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