Quotes About Ruelle

Ruelle had heard talks by Steve Smale about the horseshoe map and the chaotic possibilities of dynamical systems. He had also thought about fluid turbulence and the classic Landau picture. He suspected that these ideas were related—and contradictory.

The equations of fluid flow are nonlinear partial differential equations, unsolvable except in special cases. Yet Ruelle worked out an abstract alternative to Landau's picture, couched in the language of Smale, with images of space as a pliable material to be squeezed, stretched, and folded into shapes like horseshoes.