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Almost surely recurrent motions in the Euclidean space


Authors: Markus Kunze and Rafael Ortega
Journal: Proc. Amer. Math. Soc. 145 (2017), 4345-4351
MSC (2010): Primary 37A05, 37B20, 37J10, 37J45
DOI: https://doi.org/10.1090/proc/13556
Published electronically: March 23, 2017
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Abstract: We will show that measure-preserving transformations of $ \mathbb{R}^n$ are recurrent if they satisfy a certain growth condition depending on the dimension $ n$. Moreover, it is also shown that this condition is sharp.


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Additional Information

Markus Kunze
Affiliation: Universität Köln, Institut für Mathematik, Weyertal 86-90, D-50931 Köln, Germany

Rafael Ortega
Affiliation: Departamento de Matemática Aplicada, Universidad de Granada, E-18071 Granada, Spain

DOI: https://doi.org/10.1090/proc/13556
Keywords: Discrete dynamical systems, infinite measure space, recurrence
Received by editor(s): November 16, 2015
Received by editor(s) in revised form: October 24, 2016
Published electronically: March 23, 2017
Communicated by: Yingfei Yi
Article copyright: © Copyright 2017 American Mathematical Society

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