Abstract
We argue that computational homology can play an important role in the analysis of complicated temporal and/or spatial behavior associated with nonlinear systems. A brief description concerning the homology of spaces and maps is provided. This is followed by examples that indicate how the homology of spaces can be used to study the evolution of complicated patterns arising from numerical simulations and physical experiments. We also indicate how in conjunction with numerical computations, homology can be used to obtain computer assisted proofs in dynamics.
