Order in chaos

I will introduce a fundamental object in Dynamical Systems: the attractor of a system, and illustrate it through several examples. In particular, I will present chaotic attractors arising from real biological and physical processes, and discuss the Hénon attractor, one of the simplest models showing complex and seemingly unpredictable behavior. I will describe how the orbits of these systems behave and what makes their dynamics chaotic. A natural question is what happens when we perturb such a system slightly. Does its behavior change completely, or does some of its properties perist? In other words, how stable are these chaotic attractors?