Abundance of periodic orbits for typical impulsive semiflows

Jaqueline Siqueira (UFRJ Rio de Janeiro, Brasil)

Impulsive Dynamical Systems (IDS) can be seen as suitable mathematical models of real world phenomena
that display abrupt changes in their behaviour. More precisely, an IDS is described by three
objects: a continuous semiflow on a space X; a set D contained in X where the ow undergoes sudden
perturbations; and an impulsive function from D to X, which determines the change in the trajectory
each time it collides with the impulsive set D. A key challenge, inherent to the dynamics, is that in
general, an impulsive semiow is not continuous.
In this talk I will show that, despite several examples which display the wilderness of impulsive semi
ows, a C1 typical impulsive semiow presents some features of the ones without discontinuities,
namely, the existence of plenty of hyperbolic periodic orbits. The talk is based on a work in collaboration
with Maria Joana Torres (Minho University) and Paulo Varandas (UFBA & Porto University).