We show that Lyapunov exponent for the Sinai billiard is λ = −2 log(R)+ C + O(R log R) with C = 1 − 4 log 2 + 27/(2π) · ζ(3) where R is the radius of the circular scatterer. We consider the disk-to-disk-map of the standard configuration where the disks is centered inside a unit square.

V. KOSTRYKIN AND R. SCHRADER ABSTRACT. In this article we prove an upper bound for the Lyapunov exponent (E) and a two-sided bound for the integrated density of states N(E) at an arbitrary energy E > 0 of random Schrödinger operators in one dimension. These Schrödinger operators are given by potentials of identical shape centered at every lattice site but with non-overlapping supports and with ...

We introduce a definition of a "localization width" whose logarithm is given by the entropy of the distribution of particle component amplitudes in the Lyapunov vector. Different types of localization widths are observed, for example, a minimum localization width where the components of only two particles are dominant. We can distinguish a delocalization associated with a random distribution of...

In this note, we nd an explicit relationship between the dimension spectrum for equilibrium measures and the Lyapunov spectrum for conformal repellers. We explicitly compute the Lyapunov spectrum and show that it is a delta function. We observe that while the Lyapunov exponent exists for almost every point with respect to an ergodic measure, the set of points for which the Lyapunov exponent doe...