A symbolic simulator for hybrid equations.

In this paper, the symbolic simulation of hybrid dynamical systems is studied and an algorithm to compute symbolic solutions for such systems is presented. The tasks to perform such simulations are introduced and an algorithm to symbolically calculate a solution to a hybrid system is presented. The symbolic representation allows the proposed simulator to calculate the actual solution to the system. Benefits and drawbacks of symbolic simulation with respect to the numerical approach are presented. These statements are supported and illustrated in several examples throughout the paper

Recent advances in rigorous computation of Poincar\'e maps

In this article we present recent advances on interval methods for rigorous computation of Poincar\'e maps. We also discuss the impact of choice of Poincar\'e section and coordinate system on obtained bounds for computing Poincar\'e map nearby fixed points.Comment: 26 pages, 6 tables, 6 figure