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arXiv · 2112.11528

Symmetric Solutions to Nonlinear Vectorial 2nd Order ODE's

Ali Abdulhussein·Harry Gingold
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Abstract

It is proven that second-order vectorial nonlinear differential systems y''=f(y) , possess a continuum of symmetric solutions. They are shown to possess a continuum of even solutions. If f(y) is an odd function of y , then y''=f(y) is shown also to possess a continuum of odd solutions. The results apply to a significant family of second-order vectorial nonlinear differential systems that are not dissipative. This family of differential equations includes the celebrated N-body problem of celestial mechanics and other central force problems.

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Ali Abdulhussein, Harry Gingold. 2021-12-21. Symmetric Solutions to Nonlinear Vectorial 2nd Order ODE's. https://arxiv.org/abs/2112.11528

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