NINETY PLUS THIRTY YEARS OF NONLINEAR DYNAMICS: LESS IS MORE AND MORE IS DIFFERENT

Abstract

I review the early (1885–1975) and more recent history of dynamical systems theory, identifying key principles and themes, including those of dimension reduction, normal form transformation and unfolding of degenerate cases. I end by briefly noting recent extensions and applications in nonlinear fluid and solid mechanics, with a nod toward mathematical biology. I argue throughout that this essentially mathematical theory was largely motivated by nonlinear scientific problems, and that after a long gestation it is propagating throughout the sciences and technology.