  In the 1960s and 1970s a large part of the theory of dynamical systems
concerned the case of uniformly hyperbolic or Axiom A dynamical system and
abstract ergodic theory of smooth dynamical systems. However since around 1980
an emphasize has been on concrete examples of one-dimensional dynamical systems
with abundance of chaotic behavior (Collet &Eckmann and Jakobson). New proofs
of Jakobson's one-dimensional results were given by Benedicks and Carleson
\cite{BC85} and were considerably extended to apply to the case of H\'enon maps
by the same authors \cite{BC91}. Since then there has been a considerable
development of these techniques and the methods have been extended to the
ergodic theory and also to other dynamical systems (work by Viana, Young,
Benedicks and many others). In the cases when it applies one can now say that
this theory is now almost as complete as the Axiom A theory.
