Strange attractors in higher dimensions
- Cite this article as:
- Viana, M. Bol. Soc. Bras. Mat (1993) 24: 13. doi:10.1007/BF01231695
- 47 Downloads
We consider generic one-parameter families of diffeomorphisms on a manifold of arbitrary dimension, unfolding a homoclinic tangency associated to a sectionally dissipative saddle point (the product of any pair of eigenvalues has norm less than 1). We prove that such families exhibit strange attractors in a persistent way: for a positive Lebesgue measure set of parameter values. In the two-dimensional case this had been obtained in a joint work with L. Mora, based on and extending the results of Benedicks-Carleson on the quadratic family in the plane.