Affine endomorphisms with a dense orbit
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- by Tatsuro Kasuga PDF
- Proc. Amer. Math. Soc. 95 (1985), 659-661 Request permission
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.References
- Nobuo Aoki, Dense orbits of automorphisms and compactness of groups, Topology Appl. 20 (1985), no. 1, 1–15. MR 798440, DOI 10.1016/0166-8641(85)90030-6
- S. G. Dani, Dense orbits of affine automorphisms and compactness of groups, J. London Math. Soc. (2) 25 (1982), no. 2, 241–245. MR 653382, DOI 10.1112/jlms/s2-25.2.241
- Masahito Dateyama and Tatsuro Kasuga, Ergodic affine maps of locally compact groups, J. Math. Soc. Japan 37 (1985), no. 3, 363–372. MR 792981, DOI 10.2969/jmsj/03730363
- Paul R. Halmos, Lectures on ergodic theory, Publications of the Mathematical Society of Japan, vol. 3, Mathematical Society of Japan, Tokyo, 1956. MR 0097489
- Deane Montgomery and Leo Zippin, Topological transformation groups, Interscience Publishers, New York-London, 1955. MR 0073104
Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 95 (1985), 659-661
- MSC: Primary 54H20; Secondary 22D40
- DOI: https://doi.org/10.1090/S0002-9939-1985-0810181-5
- MathSciNet review: 810181