A C diffeomorphism with infinitely many intermingled basins


Let M be the four-dimensional compact manifold $M = T2 × S2 and let $k\ge2$. We construct a $C^\infty$ diffeomorphism $F:M\to M$ with precisely k intermingled minimal attractors $A_1,\dotsc, A_k$. Moreover the union of the basins is a set of full Lebesgue measure. This means that Lebesgue almost every point in M lies in the basin of attraction of Aj for some j, but every non-empty open set in M has a positive measure intersection with each basin. We also construct $F:M\to M$ with a countable infinity of intermingled minimal attractors. © 2005 Cambridge University Press.

Publication Title

Ergodic Theory and Dynamical Systems