Many intermingled basins in dimension 3

Abstract

We construct a diffeomorphism of ${\mathbb{T}}^3$ admitting any finite or countable number of physical measures with intermingled basins. The examples are partially hyperbolic with splitting $T{\mathbb{T}}^3=E^{cs}\oplus E^u$ and can be made volume hyperbolic and topologically mixing.

20 pages, 4 figures. Some changes made after referee report. To appear in Israel J. of Math