For dissipative dynamics, chaos is defined as the existence of strange attractors.
Chaotic behaviour was often numerically observed, but the first mathematical proof
of the existence, with positive probability (persistence), of a strange attractor was
given by Benedicks and Carleson for the Henon family, at the begining of 1990's. A
short time later. Mora and Viana extended the proof of Benedicks and Carleson to the
Henon-like families in order to demonstrate that a strange attractor is also persistent
in generic one-parameter families of surface diffeomorphisms unfolding a homoclinic
tangency, as conjectured by Palis. In the present book, we prove the coexistence
and persistence of any number of strange attractors in a simple three-dimensional
scenario. Moreover, infinitely many of them exist simultaneously.
Besides proving this new non-hyperbolic phenomenon, another goal of this book
is to show how the Benedicks-Carleson proof can be extended to families different
from the Henon-like ones.