We prove that the Newhouse phenomenon has a codimension 2 nature.
Namely, there exist codimension 2 laminations of maps with infinitely many sinks.
The leaves of the laminations are smooth and the sinks move simultaneously along the leaves.
These Newhouse laminations occur in unfoldings of rank-one homoclinic tangencies.
As consequence, in the space of polynomial maps, there are examples of:
- two dimensional Hénon maps with finitely many sinks and one strange attractor,
- Hénon maps, in any dimension, with infinitely many sinks,
- quadratic Hénon-like maps with infinitely many sinks and a period doubling attractor,
- quadratic Hénon-like maps with infinitely many sinks and a strange attractor,
- a non trivial analytic one-parameter family of quadratic Hénon-like maps with infinitely many sinks,
- two dimensional Hénon maps with finitely many sinks and two period doubling attractors.