On shadowing and chain recurrence in linear dynamics Article Swipe
Nilson C. Bernardes
,
Alfredo Peris
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.1016/j.aim.2024.109539
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.1016/j.aim.2024.109539
[EN] In the present work we study the concepts of shadowing and chain recurrence in the setting of linear dynamics. We prove that shadowing and finite shadowing always coincide for operators on Banach spaces, but we exhibit operators on the Frechet space H(C) of entire functions that have the finite shadowing property but do not have the shadowing property. We establish a characterization of mixing for continuous maps with the finite shadowing property in the setting of uniform spaces, which implies that chain recurrence and mixing coincide for operators with the finite shadowing property on any topological vector space. We establish a characterization of dense distributional chaos for operators with the finite shadowing property on Frechet spaces. As a consequence, we prove that if a Devaney chaotic (resp. a chain recurrent) operator on a Frechet space (resp. on a Banach space) has the finite shadowing property, then it is densely distributionally chaotic. We obtain complete characterizations of chain recurrence for weighted shifts on Frechet sequence spaces. We prove that generalized hyperbolicity implies periodic shadowing for operators on Banach spaces. Moreover, the concepts of shadowing and periodic shadowing coincide for unilateral weighted backward shifts, but these notions do not coincide in general, even for bilateral weighted shifts. (c) 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY -NC license (http:// creativecommons .org /licenses /by -nc /4 .0/).
Related Topics
Concepts
Mathematics
Banach space
Property (philosophy)
Characterization (materials science)
Pure mathematics
Space (punctuation)
Chain (unit)
Vector space
Approximation property
Chaotic
Mathematical analysis
Computer science
Epistemology
Nanotechnology
Physics
Operating system
Artificial intelligence
Materials science
Philosophy
Astronomy
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- Language
- en
- Landing Page
- https://doi.org/10.1016/j.aim.2024.109539
- OA Status
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- Cited By
- 8
- References
- 47
- Related Works
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- OpenAlex ID
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All OpenAlex metadata
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https://openalex.org/W4391991344Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.1016/j.aim.2024.109539Digital Object Identifier
- Title
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On shadowing and chain recurrence in linear dynamicsWork title
- Type
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articleOpenAlex work type
- Language
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enPrimary language
- Publication year
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2024Year of publication
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2024-02-21Full publication date if available
- Authors
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Nilson C. Bernardes, Alfredo PerisList of authors in order
- Landing page
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https://doi.org/10.1016/j.aim.2024.109539Publisher landing page
- Open access
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YesWhether a free full text is available
- OA status
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hybridOpen access status per OpenAlex
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https://doi.org/10.1016/j.aim.2024.109539Direct OA link when available
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Mathematics, Banach space, Property (philosophy), Characterization (materials science), Pure mathematics, Space (punctuation), Chain (unit), Vector space, Approximation property, Chaotic, Mathematical analysis, Computer science, Epistemology, Nanotechnology, Physics, Operating system, Artificial intelligence, Materials science, Philosophy, AstronomyTop concepts (fields/topics) attached by OpenAlex
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8Total citation count in OpenAlex
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2025: 3, 2024: 5Per-year citation counts (last 5 years)
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47Number of works referenced by this work
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10Other works algorithmically related by OpenAlex
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