We provide general methods for explicitly constructing strict Lyapunov functions for fully nonlinear slowly time-varying systems. Our results apply to cases where the given dynamics and corresponding frozen dynamics are not necessarily exponentially stable. This complements our previous Lyapunov function constructions for rapidly time-varying dynamics. We also explicitly construct input-to-stat...

The moment-transfer approach is a standard tool for deriving limit laws of sequences of random variables satisfying a distributional recurrence. However, so far the approach could not be applied to certain “one-sided" recurrences with slowly varying moments and normal limit law. In this paper, we propose a modified version of the moment-transfer approach which can be applied to such recurrences...

ON SLOWLY VARYING STOKES WAVES by VINCENT HWA-HING CHU In this thesis investigations are made on the theory of a train of slowly modulated gravity waves propagating over uneven bottom topography. The primary object is to study the interplay of amplitude dispersion the frequency dispersion in waves on the surface of water where the depth is not too shallow compared to a typical wave length. The ...