Some universality results for dynamical systems
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- by Udayan B. Darji and Étienne Matheron PDF
- Proc. Amer. Math. Soc. 145 (2017), 251-265 Request permission
Abstract:
We prove some “universality” results for topological dynamical systems. In particular, we show that for any continuous self-map $T$ of a perfect Polish space, one can find a dense, $T$-invariant set homeomorphic to the Baire space $\mathbb {N}^{\mathbb {N}}$; that there exists a bounded linear operator $U: \ell \rightarrow \ell$ such that any linear operator $T$ from a separable Banach space into itself with $\Vert T\Vert \leq 1$ is a linear factor of $U$; and that given any $\sigma$-compact family ${\mathcal F}$ of continuous self-maps of a compact metric space, there is a continuous self-map $U_{\mathcal F}$ of $\mathbb {N}^{\mathbb {N}}$ such that each $T\in {\mathcal F}$ is a factor of $U_{\mathcal F}$.References
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Additional Information
- Udayan B. Darji
- Affiliation: Department of Mathematics, University of Louisville, Louisville, Kentucky 40292
- MR Author ID: 318780
- ORCID: 0000-0002-2899-919X
- Email: ubdarj01@louisville.edu
- Étienne Matheron
- Affiliation: Laboratoire de Mathématiques de Lens, Université d’Artois, Rue Jean Souvraz S. P. 18, 62307 Lens, France
- MR Author ID: 348460
- Email: etienne.matheron@univ-artois.fr
- Received by editor(s): December 3, 2015
- Received by editor(s) in revised form: March 16, 2016
- Published electronically: July 12, 2016
- Additional Notes: The first author would like to acknowledge the hospitality and financial support of Université d’Artois
- Communicated by: Mirna Džamonja
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 251-265
- MSC (2010): Primary 37B99, 54H20; Secondary 54C20, 47A99
- DOI: https://doi.org/10.1090/proc/13225
- MathSciNet review: 3565377