The Legacy of the Cartwright-Littlewood Collaboration

TL;DR

This paper reviews the historical and mathematical significance of Cartwright and Littlewood's 1945 work on the forced van der Pol equation, highlighting their pioneering insights into chaos and their influence on subsequent research.

Contribution

It provides a comprehensive overview of the original 1945 investigation, its context, and its lasting impact on dynamical systems theory and related fields.

Findings

Early description of chaotic behavior in dissipative systems

Influence on subsequent chaos theory research

Historical insight into Cartwright and Littlewood's 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 \begin{equation*} \ddot{y}-k(1-y^2)\dot{y}+y = b \lambda k \cos(\lambda t+a) \end{equation*} in which $b,\lambda,k,a$ are parameters with $k$ 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 twelve 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.