Dimensions of structurally stable and critical strange non-chaotic attractors

Abstract

We provide evidence that the box-counting dimension of a structurally stable strange non-chaotic attractor (SNA) of pinched skew product type is equal to 2 by showing that it has non-negligible area. The argument presented is made more accurate in the study of a piecewise linear SNA. Furthermore we provide evidence that the fractal dimension of a critical SNA is not equal to 2, but in fact lies between 1 and 2. We numerically calculate the box-counting dimension for several critical SNAs, providing further evidence to support this conjecture.