Title: The Legacy of Cartwright and Littlewood
Abstract: This talk is based on my contribution to a centennial volume of the Journal of the London Mathematical Society describing mathematical developments spawned by selected papers.
Mary Cartwright and John E. Littlewood published a seminal paper on the forced van der Pol equation in 1945, the birth year of “Coupled 80”.
Their paper describes work begun in response to a request by the British Radio Research Board for mathematicians to help during World War II. It presents a “preliminary survey” of the first mathematical analysis of chaos in a non-conservative dynamical system of differential equations. They inspired further work on dynamical systems, including Smale’s famous horseshoe example. The details of their work appeared only in 1957 in a paper whose complexity is infamous. I recount the history of this work along with my contributions with collaborators to extend it, recasting the results to be much more accessible.