The liapunov dimension of strange attractors

Many papers have been published recently on studies of dynamical processes in which the attracting sets appear quite strange. In this paper the question of estimating the dimension of the attractor is addressed. While more general conjectures are made here, particular attention is paid to the idea that if the Jacobian determinant of a map is greater than one and a ball is mapped into itself, then generically, the attractor will have positive two-dimensional measure, and most of this paper is devoted to presenting cases with such Jacobians for which the attractors are proved to have non-empty interior.