Point vortices are singular solutions of the 2-dimensional incompressible Navier-Stokes equations which were first studied by Helmholtz. While the dynamics of point vortices is fairly straightforward, these objects can create complex dynamics in the velocity field of a flow, producing regions where passive particles can have either regular or chaotic trajectories. In fact, it is known that around each vortex there exists what it is usually called a stability island, where the motion of passive particles is always regular. Furthermore, the boundaries of these islands constitute barriers to particle motion.
In this talk, we will present the basic concepts behind vortex dynamics and characterise the stability islands in systems of two vortices. We will further extend the discussion into systems with more than two vortices and systems with viscous vortices. If time allows, we will also show a simple example of how we can take advantage of a point vortex to transport a particle between two points in space while minimising the energy of the process.