Abstract

This thesis studies different types of dimensions of attractors in low dimensional dissipative dynamical systems. Some of them can be calculated by looking directly at the attractor, other by looking at the system, taking or not into account a probability distribution. We give some simple examples to make the ideas clear, but the generalized baker's transformation is taken as a model for such studies. This transformation is used to illustrate some conjectures about typical chaotic attractor. This thesis may be considered as a partial report of the seminal article of Farmer et al (12)