What is Dynamics about? In broad terms, the goal of Dynamics is to
describe the long term evolution of systems for which an "infinitesimal"
evolution rule is known. Examples and applications arise from all
branches of science and technology, like physics, chemistry, economics,
ecology, communications, biology, computer science, or meteorology, to
mention just a few. These systems have in common the fact that each
possible state may be described by a finite (or infinite) number of
observable quantities, like position, velocity, temperature,
concentration, population density, and the like. Thus, m the space of
states (phase space) is a subset M of an Euclidean space M . Usually,
there are some constraints between these quantities: for instance, for
ideal gases pressure times volume must be proportional to temperature.
Then the space M is often a manifold, an n-dimensional surface for some
n