Ermakov-Painleve IV coupled systems are introduced and associated Ermakov-type invariants isolated. These used to obtain systematic reduction of the system in terms canonical Painleve equation. The procedure is applied a symmetry derivative resonant nonlinear Schro dinger triad incorporating de Broglie-Bohm potential terms.

Results from classical dynamical systems are generalized to hybrid dynamical systems. The concept of ! limit set is introduced for hybrid systems and is used to prove new results on invariant sets and stability, where Zeno and non-Zeno hybrid systems can be treated within the same framework. As an example, LaSalle's Invariance Principle is extended to hybrid systems. Zeno hybrid systems are dis...