Lyapunov regularity via singular values

Barreira, Luis; Valls, Claudia

doi:10.1090/tran/6910

Lyapunov regularity via singular values
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by Luis Barreira and Claudia Valls PDF

Trans. Amer. Math. Soc. 369 (2017), 8409-8436 Request permission

Abstract:

For a nonautonomous linear dynamics, we study the relation between Lyapunov regularity and the exponential growth rates of the singular values. In particular, for a tempered dynamics, we obtain lower and upper estimates for the Lyapunov exponents in terms of the growth rates. The proof is based on the somewhat unexpected existence of a structure of Oseledets type for any nonregular dynamics. Moreover, we show that any possible values of the Lyapunov exponent and of the growth rates are attained by some bounded sequence of matrices. As an application of our results, we give a simple proof of various characterizations of Lyapunov regularity as well as a new characterization. We consider both discrete and continuous time.

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