Tapia Garcia, S. (2024). Recurrence and vectors escaping to infinity for Lipschitz operators. Journal of Mathematical Analysis and Applications, 530(2), Article 127658. https://doi.org/10.1016/j.jmaa.2023.127658
E105-04 - Forschungsbereich Variationsrechnung, Dynamische Systeme und Operations Research
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Journal:
Journal of Mathematical Analysis and Applications
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ISSN:
0022-247X
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Date (published):
15-Feb-2024
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Number of Pages:
21
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Publisher:
ACADEMIC PRESS INC ELSEVIER SCIENCE
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Peer reviewed:
Yes
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Keywords:
Dynamics of linear operators; Lipschitz-free spaces; Recurrent points
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Abstract:
We investigate dynamical properties of linear operators that are obtained as the linearization of Lipschitz self-maps defined on a pointed metric space. These operators are known as Lipschitz operators. More precisely, for a Lipschitz operator fˆ, we study the set of recurrent vectors and the set of vectors μ such that the sequence (‖fˆn(μ)‖)n goes to infinity. As a consequence of our results we get that there is no wild Lipschitz operator. Furthermore, several examples are presented illustrating our ideas. We highlight the cases when the underlying metric space is a connected subset of R or a subset of Zd. We end this paper studying some topological properties of the set of Lipschitz operators.
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Project title:
Unilateralität und Asymmetrie in der Variationsanalyse: P 36344N (FWF Fonds zur Förderung der wissenschaftlichen Forschung (FWF))