1. Dynamics of nonlinear systems. Dissipative systems

In this article, we focus on so-called dissipative systems, although Hamiltonian studies are still relevant.

The key feature of dissipative systems is that Liouville's theorem (see history box opposite) is no longer satisfied. Under the effect of dissipation, an initial volume of the phase space tends asymptotically towards an object, of zero volume, called an attractor. It is also very often the case that a dynamical system originally evolving in a phase space of infinite dimension ends up, under the effect of dissipation, evolving in a phase space of finite or even low dimension