## Locally compact flows on connected manifolds

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- by Khadija Ben Rejeb PDF
- Conform. Geom. Dyn.
**25**(2021), 253-260 Request permission

## Abstract:

In this paper, we completely characterize locally compact flows $G$ of homeomorphisms of connected manifolds $M$ by proving that they are either circle groups or real groups. For $M = \mathbb R^m$, we prove that every recurrent element in $G$ is periodic, and we obtain a generalization of the result of Yang [*Hilbert’s fifth problem and related problems on transformation groups*, American Mathematical Society, Providence, RI, 1976, pp. 142–146.] by proving that there is no nontrivial locally compact flow on $\mathbb R^m$ in which all elements are recurrent.

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## Additional Information

**Khadija Ben Rejeb**- Affiliation: Higher School of Sciences and Technology of Hammam Sousse, 4011 Hammam Sousse, Tunisia
- MR Author ID: 912473
- Email: kbrjeb@yahoo.fr, khadija.benrejeb@essths.u-sousse.tn
- Received by editor(s): April 19, 2020
- Received by editor(s) in revised form: April 1, 2021, and September 5, 2021
- Published electronically: December 9, 2021
- © Copyright 2021 American Mathematical Society
- Journal: Conform. Geom. Dyn.
**25**(2021), 253-260 - MSC (2020): Primary 37B05, 37B20, 57S05, 57S10
- DOI: https://doi.org/10.1090/ecgd/366
- MathSciNet review: 4349915