 Singular ValuesLuís Barreira
Chapter Chapter 6 in Lyapunov Exponents, 2017, pp 115-135 from Springer Abstract: Abstract In this chapter we go back to the core of the theory of Lyapunov exponents and the theory of regularity. It has the main purpose of describing in detail the relation between singular values and Lyapunov exponents, both for discrete and continuous time. We first show that the general inequalities between the values of the Lyapunov exponent and of the upper exponential growth rates of the singular values are the best possible. More precisely, we show that any sets of numbers satisfying these general inequalities are realized as the values of the Lyapunov exponent and of the upper exponential growth rates of the singular values of some bounded sequence of matrices. We then establish one of the central results of the book: for an arbitrary tempered sequence of matrices, and so possibly nonregular, we obtain general inequalities between the values of the Lyapunov exponent and the lower and upper exponential growth rates of the singular values (and not only upper). These inequalities are obtained as a consequence of the existence of a structure of Oseledets type that is present even for a nonregular sequence. We also consider briefly the case of continuous time and we obtain corresponding versions of the results. Date: 2017 There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it. Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-71261-1_6 Ordering information: This item can be ordered from DOI: 10.1007/978-3-319-71261-1_6 Access Statistics for this chapter More chapters in Springer Books from Springer |
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