The second iterate of a map with dense orbit

Author:
Paul S. Bourdon

Journal:
Proc. Amer. Math. Soc. **124** (1996), 1577-1581

MSC (1991):
Primary 54H20; Secondary 47A15, 58F13

DOI:
https://doi.org/10.1090/S0002-9939-96-03648-9

MathSciNet review:
1363443

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Abstract: Suppose that is a Hausdorff topological space having no isolated points and that is continuous. We show that if the orbit of a point under is dense in while the orbit of under is not, then the space decomposes into three sets relative to which the dynamics of are easy to describe. This decomposition has the following consequence: suppose that has dense orbit under and that the closure of the set of points of having odd period under has nonempty interior; then has dense orbit under .

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Additional Information

**Paul S. Bourdon**

Affiliation:
Department of Mathematics, Washington and Lee University, Lexington, Virginia 24450

Email:
pbourdon@wlu.edu

DOI:
https://doi.org/10.1090/S0002-9939-96-03648-9

Received by editor(s):
June 1, 1994

Communicated by:
James E. West

Article copyright:
© Copyright 1996
American Mathematical Society