Manuscript submitted to Website: www.aimSciences.org DCDS Supplement Volume 2007 pp. 1–4 SYMMETRIC EVENT COLLISIONS IN DYNAMICAL SYSTEMS WITH DELAYED SWITCHES

We study dynamical systems that switch between two different vector fields depending on a discrete variable. If the two vector fields have lin-early unstable fixed points and the switch is subject to a hysteresis and to a delay one expects the system to switch periodically back and forth between the two vector fields, always switching at certain submanifolds of the state space of the vector fields. This is true as long as the delay is sufficiently small. When the delay reaches a problem-dependent critical value so-called event collisions occur. We show that at these event colli-sions the switching manifolds can increase their dimension, giving rise to higher-dimensional dynamics near the periodic orbit than expected. In many practical applications in control engineering the dynamical system has additional symmetry, which adds difficulty in the analysis because event collisions generically occur at several points along the periodic orbit simultaneously. 1. Introduction. Dynamica