- 01-14 David Damanik, Robert Sims, Gunter Stolz
- Lyapunov exponents in continuum Bernoulli-Anderson models
Jan 10, 01
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Abstract. We study one-dimensional, continuum Bernoulli-Anderson models with
general single-site potentials and prove positivity of the
Lyapunov exponent away from a discrete set of critical energies.
The proof is based on F\"urstenberg's Theorem. The set of critical
energies is described explicitly in terms of the transmission and
reflection coefficients for scattering at the single-site
potential. In examples we discuss the asymptotic behavior of
generalized eigenfunctions at critical energies.