Tempered Dichotomies

Luís Barreira
Additional contact information
Luís Barreira: Universidade de Lisboa, Instituto Superior Técnico

Chapter Chapter 8 in Lyapunov Exponents, 2017, pp 169-186 from Springer

Abstract: Abstract In this chapter we start describing the important relation between nonzero Lyapunov exponents and hyperbolicity. More precisely, we discuss how the existence of a nonzero Lyapunov exponent gives rise to hyperbolicity and how this relates to the theory of regularity. We start with the simpler case of sequences of matrices with a negative Lyapunov exponent, for which the exposition is simpler. We also consider the notion of strong tempered spectrum of a sequence of matrices and we describe all its possible forms. This spectrum can be seen as a nonuniform version of the Sacker–Sell spectrum, which in its turn can be described as a nonautonomous version of the spectrum of a matrix. In the case of a regular sequence of matrices, we show that the strong tempered spectrum is simply the set of values of the Lyapunov exponent. We also describe briefly versions of the former results for continuous time.

Date: 2017
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-71261-1_8

Ordering information: This item can be ordered from
http://www.springer.com/9783319712611

DOI: 10.1007/978-3-319-71261-1_8

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().