<div class="csl-bib-body">
<div class="csl-entry">Tapia Garcia, S. (2024). Recurrence and vectors escaping to infinity for Lipschitz operators. <i>Journal of Mathematical Analysis and Applications</i>, <i>530</i>(2), Article 127658. https://doi.org/10.1016/j.jmaa.2023.127658</div>
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dc.identifier.issn
0022-247X
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/189736
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dc.description.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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dc.description.sponsorship
FWF Fonds zur Förderung der wissenschaftlichen Forschung (FWF)
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dc.language.iso
en
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dc.publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
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dc.relation.ispartof
Journal of Mathematical Analysis and Applications
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dc.subject
Dynamics of linear operators
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dc.subject
Lipschitz-free spaces
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dc.subject
Recurrent points
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dc.title
Recurrence and vectors escaping to infinity for Lipschitz operators