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Continuity of the Lyapunov Exponent for analytic quasi-perodic cocycles with singularities
the Lyapunov Exponent analytic quasi-perodic cocycles singularities Harper's model
2011/7/29
Abstract: We prove that the Lyapunov exponent of quasi-periodic cocyles with singularities behaves continuously over the analytic category. We thereby generalize earlier results, where singularities w...
We study the effect of a random perturbation on a one-parameter family of dynamical systems whose behavior in the absence of perturbation is ill understood.We provide conditions under which the pertur...
Positive Lyapunov exponent by a random perturbation
Lyapunov exponent random perturbation
2010/12/28
We study the effect of a random perturbation on a one-parameter family of dynamical systems whose behavior in the absence of perturbation is ill understood.We provide conditions under which the pertur...
Quenched Lyapunov exponent for the parabolic Anderson model in a dynamic random environment
Quenched Lyapunov exponent parabolic Anderson model
2010/11/9
We continue our study of the parabolic Anderson equation $\partial u/\partial t = \kappa\Delta u + \gamma\xi u$ for the space-time field $u\colon\,\Z^d\times [0,\infty)\to\R$, where $\kappa \in [0,\in...