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
These Newhouse laminations occur in unfoldings of rank-one homoclinic
tangencies. As a consequence,
in the space of polynomial maps, there are examples of:
The first lecture will discuss topological aspects of two dimensional dynamics.
This part will give a context for the Newhouse Laminations.
The second part will discuss in more detail the construction of the Newhouse Laminations.
- 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 one period doubling attractor,
- quadratic Hénon-like maps with infinitely many sinks and one strange attractor,
- two dimensional Hénon maps with finitely many sinks and two period doubling attractors,
- quadratic Hénon-like maps with finitely many sinks, two period doubling attractors and one strange attractor.