Infinitely many strange attractors in higher dimensions

DDIC

Keywords: Homoclinic tangency | strange attractors | sectionally dissipative

In this work we show, on a manifold of any dimension, that arbitrarily near any smooth diffeomorphism with a homoclinic tangency associated to a sectionally dissipative fixed (or periodic) point (i.e. the product of any pair of eigenvalues has norm less than 1), there exists a diffeomorphism exhibiting infinitely many Hénon-like strange attractors. In the two-dimensional case this has been proved by Colii in 1998. We also show a parameteric version of this result is true.

Anexos:

• strge-art.ps