The Legacy of the Cartwright-Littlewood Collaboration
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912418838347776 |
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| author | Guckenheimer, John |
| author_facet | Guckenheimer, John |
| contents | 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 λk \cos(λt+a) \end{equation*} in which $b,λ,k,a$ 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_06889 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Legacy of the Cartwright-Littlewood Collaboration Guckenheimer, John Dynamical Systems 34C15, 34E13, 34E17, 37-03, 37D45, 37N20 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 λk \cos(λt+a) \end{equation*} in which $b,λ,k,a$ 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. |
| title | The Legacy of the Cartwright-Littlewood Collaboration |
| topic | Dynamical Systems 34C15, 34E13, 34E17, 37-03, 37D45, 37N20 |
| url | https://arxiv.org/abs/2506.06889 |