Advertisement

Comparison of Lyapunov Exponents and Boundaries

  • Philippe Bougerol
  • Jean Lacroix
Part of the Progress in Probability and Statistics book series (PRPR, volume 8)

Abstract

In the preceding chapter we have given a criterion ensuring that the two upper Lyapunov exponents are distinct. It will give us all we need for the study of limit theorems. But a sharp study of the behaviour at infinity of the random products S requires a precise knowledge of the relations between all the exponents. For instance they provide all the limit values of \( \frac{1}{n}\;Log\;\left\| {{S_{n}}\left( \omega \right)x} \right\| \) , when ω is kept fixed and x runs through ℝd (Osseledec’s theorem) and determine the possible boundaries towards which Sn converges.

Keywords

Probability Measure Lyapunov Exponent Closed Subgroup Invariant Distribution Invariant Probability Measure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Birkhäuser Boston, Inc. 1985

Authors and Affiliations

  • Philippe Bougerol
    • 1
  • Jean Lacroix
    • 2
  1. 1.UER de MathématiquesUniversité Paris 7ParisFrance
  2. 2.Département de MathématiquesUniversité de Paris XIIIVilletaneuseFrance

Personalised recommendations