Almost surely recurrent motions in the Euclidean space
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- by Markus Kunze and Rafael Ortega PDF
- Proc. Amer. Math. Soc. 145 (2017), 4345-4351 Request permission
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.References
- M. Brown, Homeomorphisms of two-dimensional manifolds, Houston J. Math. 11 (1985), no. 4, 455–469. MR 837985
- Michael Colvin and Kent Morrison, A symplectic fixed point theorem on open manifolds, Proc. Amer. Math. Soc. 84 (1982), no. 4, 601–604. MR 643757, DOI 10.1090/S0002-9939-1982-0643757-6
- D. Dolgopyat, Lectures on bouncing balls, lecture notes for a course in Murcia, 2013; available at http://www2.math.umd.edu/$\sim$dolgop/BBNotes.pdf
- M. Kunze and R. Ortega, Escaping orbits are rare in the quasi-periodic Fermi-Ulam ping-pong, preprint, 2015; available at http://www.ugr.es/$\sim$ecuadif/fuentenueva.htm
- R. Ortega, Topology of the Plane and Periodic Differential Equations. Chapter 3. Free embeddings of the plane, book project; available at http://www.ugr.es/$\sim$ecuadif/files/ libro3.pdf
Additional Information
- Markus Kunze
- Affiliation: Universität Köln, Institut für Mathematik, Weyertal 86-90, D-50931 Köln, Germany
- MR Author ID: 357041
- Rafael Ortega
- Affiliation: Departamento de Matemática Aplicada, Universidad de Granada, E-18071 Granada, Spain
- 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
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 4345-4351
- MSC (2010): Primary 37A05, 37B20, 37J10, 37J45
- DOI: https://doi.org/10.1090/proc/13556
- MathSciNet review: 3690618