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1. Spectra and Examples

  • 2024
  • OriginalPaper
  • Chapter
Published in:
Authors
Luís Barreira
Claudia Valls
Published in
Spectra and Normal Forms
Publisher
Springer Nature Switzerland

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Abstract

In this chapter we introduce the notions of tempered exponential dichotomy and of tempered spectrum for a sequence of \(d \times d\) matrices that need not be invertible. The tempered spectrum can be thought of as a nonautonomous version of the usual notion of spectrum for a single matrix. We also describe all possible forms of the tempered spectrum and we give explicit examples of all of them. More precisely, for each possible form we describe explicitly a sequence of invertible matrices with that tempered spectrum.

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next chapter Asymptotic Behavior
Title
Spectra and Examples
Authors
Luís Barreira
Claudia Valls
Copyright Year
2024
Book
Spectra and Normal Forms

Print ISBN: 978-3-031-51896-6

Electronic ISBN: 978-3-031-51897-3

Copyright Year: 2024

DOI
https://doi.org/10.1007/978-3-031-51897-3_1
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