DENSITY OF POSITIVE LYAPUNOV EXPONENTSFOR SL(2,R)-COCYCLES

摘要

The understanding of the frequency of hyperbolic behavior is one of the central themes in dynamics [By]. Precise questions can be posed on several levels, for instance, in the context of area-preserving maps: 1. Under suitable smoothness assumptions, quasiperiodicity, and hence the ab-sence of any kind of hyperbolicity, is non-negligible in a measure-theoretical sense [Kol] (under suitable smoothness assumptions).2. In low regularity (0), failure of non-uniform hyperbolicity (here non-uniform hyperbolicity can be understood as positivity of the metric entropy) is a fairly robust phenomenon in the topological sense [B].