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Lyapunov Sequences

In: Lyapunov Exponents

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  • Luís Barreira

    (Universidade de Lisboa, Instituto Superior Técnico)

Abstract

In this chapter we show how the existence of a strong tempered dichotomy follows from the existence of a strict quadratic Lyapunov sequence. Starting with the simpler case of a tempered dichotomy, we show in this case that the notion can be completely characterized in terms of the existence of a strict quadratic Lyapunov sequence. This includes explicitly constructing such a sequence for any tempered dichotomy. The chapter can be considered as a version for a single trajectory of corresponding results for cocycles over a measure-preserving transformation. Unsurprisingly, the powerful tools of ergodic theory allow that the corresponding hypotheses in the notion of a Lyapunov function are weaker in the context of ergodic theory.

Suggested Citation

  • Luís Barreira, 2017. "Lyapunov Sequences," Springer Books, in: Lyapunov Exponents, chapter 0, pages 187-202, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-71261-1_9
    DOI: 10.1007/978-3-319-71261-1_9
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