The legacy of the Cartwright–Littlewood collaboration

Abstract Mary L. Cartwright and John E. Littlewood published a short “preliminary survey” in 1945 describing results of their investigation of the forced van der Pol equation in which are parameters with large. Their description of dynamical behavior now known as chaos in this dissipative dynamical system was a landmark in dynamical systems theory. Littlewood's “monster paper” containing the details of their investigation finally appeared 12 years later in the journal Acta Mathematica. I review here the context in which Cartwright and Littlewood worked when they wrote their 1945 paper and the enduring mathematical legacy of their discoveries. I also give brief pointers to research they inspired in other application areas.