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arXiv · 2506.06889

The Legacy of the Cartwright-Littlewood Collaboration

John Guckenheimer
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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.

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John Guckenheimer. 2025-06-07. The Legacy of the Cartwright-Littlewood Collaboration. https://arxiv.org/abs/2506.06889

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