  The emphasis of this course is on pluripotential methods in complex dynamics
in higher dimension. They are based on the compactness properties of
plurisubharmonic functions and on the theory of positive closed currents.
Applications of these methods are not limited to the dynamical systems that we
consider here. We choose to show their effectiveness and to describe the theory
for two large families of maps. The first chapter deals with holomorphic
endomorphisms of the projective space P^k. We establish the first properties
and give several constructions for the Green currents and the equilibrium
measure \mu. The emphasis is on quantitative properties and speed of
convergence. We then treat equidistribution problems and establish ergodic
properties of \mu: K-mixing, exponential decay of correlations for various
classes of observables, central limit theorem and large deviations theorem.
Finally, we study the entropy, the Lyapounov exponents and the dimension of
\mu. The second chapter develops the theory of polynomial-like maps in higher
dimension. We introduce the dynamical degrees and construct the equilibrium
measure \mu of maximal entropy. Then, under a natural assumption, we prove
equidistribution properties of points and various statistical properties of the
measure \mu. The assumption is stable under small pertubations on the map. We
also study the dimension of \mu, the Lyapounov exponents and their variation.
Our aim is to get a self-contained text that requires only a minimal
background. In order to help the reader, an appendix gives the basics on p.s.h.
functions, positive closed currents and super-potentials on projective spaces.
Some exercises are proposed and an extensive bibliography is given.
