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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Affine endomorphisms with a dense orbit


Author: Tatsuro Kasuga
Journal: Proc. Amer. Math. Soc. 95 (1985), 659-661
MSC: Primary 54H20; Secondary 22D40
MathSciNet review: 810181
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Abstract: For a continuous endomorphism $ f$ on a locally compact group $ X$ and $ a \in X$, we define an affine endomorphism $ {f_a}:X \to X$. We prove that if $ {f_a}$ is not one to one and if $ \left( {X,{f_a}} \right)$ has a dense orbit then $ X$ is compact.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0810181-5
PII: S 0002-9939(1985)0810181-5
Article copyright: © Copyright 1985 American Mathematical Society