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• W2318340538 abstract "- Balthasar van der Pol's experiments on electrical circuits during the 1920s and 1930s opened an interesting chapter in the history of dynamics. The need for advancements in radio technology made van der Pol's work pertinent and his research stimulated mathematical interest in nonlinear oscillators. In particular, van der Pol's work caught the attention of Cambridge mathematicians M. L. Cartwright and J. E. Littlewood. Topology and Poincare's transformation theory provided a key to analyzing behavior of nonlinear oscillators and dissipative systems. Resulting mathematical techniques have played a significant role in the development of the modern theory of dynamical systems and chaos. In addition, nonlinear oscillator theory has led to the development of radio, radar, and laser technology. The collaboration between Cartwright and Littlewood began just before World War II and lasted approximately ten years. They published four joint papers, and individually published several other papers based on joint work. Their collaboration produced some of the earliest rigorous work in the field of large parameter theory. They were among the first mathematicians to recognize that topological and analytical methods could be combined to efficiently obtain results for various problems in differential equations, and their results helped inspire the construction of Smale's horseshoe diffeomorphism.l Their names can be included with those mathematicians, including Levinson, Lefschetz, Minorsly, Liapounov, KIyloff, Bogolieuboff, Denjoy, Birkhoff, and Poincare, whose work provided an impetus to the development of modern dynamical theory. Cartwright knew G. H. Hardy at Oxford before she met Littlewood. Cartwright joined a special group when she began to attend Hardy's Friday class at New College in January, 1928. The participants included Gertrude Stanley, John Evelyn, E. H. Linfoot, L. S. Bosenquet, Frederick Brand, and Tirukkannapuram Vijayarhagavan. Nearly all completed their D. Phils by the summer of 1928. The universal feeling among the participants was that they were studying under a very great man who had not yet been recognized fully. Cartwright appreciated Hardy's stylE and philosophy of mathematics. She recalled that he took immense trouble with his students whether they were good, bad, or indifferent. Once, when she had produced an obviously fallacious result, Hardy remarked, Let's see, there's always hope when you get a sharp contradiction.2 Hardy became Cartwright's initial thesis advisor and she finished with E. C. Titschmarsh when Hardy went on leave to Princeton. Cartwright first met Littlewood in June of 1930 when he went to Oxford to examine her for her Doctor of Philosophy degree. The following October she went to Girton College, Cambridge on a three-year research fellowship. She attended a" @default.
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• W2318340538 date "1996-12-01" @default.
• W2318340538 modified "2023-09-23" @default.
• W2318340538 title "The Mathematical Collaboration of M. L. Cartwright and J. E. Littlewood" @default.
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• W2318340538 doi "https://doi.org/10.1080/00029890.1996.12004828" @default.
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