The set of all iterates is nowhere dense in

Author:
A. M. Blokh

Journal:
Trans. Amer. Math. Soc. **333** (1992), 787-798

MSC:
Primary 26A18; Secondary 58F08

DOI:
https://doi.org/10.1090/S0002-9947-1992-1153009-7

MathSciNet review:
1153009

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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that if a mixing map belongs to the -closure of the set of iterates and , then is an iterate itself. Together with some one-dimensional techniques it implies that the set of all iterates is nowhere dense in giving the final answer to the question of A. Bruckner, P. Humke and M. Laczkovich.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1992-1153009-7

Keywords:
Iterates of maps,
mixing maps,
periodic points

Article copyright:
© Copyright 1992
American Mathematical Society