In the study of nonlinear systems, one has a number of tools at use. These tools can be categorized into three distinct areas:

1. Geometry: Fractals and the measure of fractal dimensions can be used to study the nature of attractors.
2. Dynamics: Lyaponov exponents can be used to understand the dynamics of attractors
3. Topology: Topological tools have been found to provide powerful means to classifying strange attractors.