Symbolic computation in nonlinear dynamics

This paper gives examples of how computer algebra systems can help us to understand nonlinear dynamical systems and their numerical simulations. We caution against naive use of exact arithmetic, but we give examples where elementary use is helpful. We also look at the use of polynomial computations — such as factoring, computation of discriminants, and Gröbner bases — in bifurcation studies.This paper is dedicated to the memory of M. A. H. Nerenberg (1936–1993).