XXXVIII Workshop on Geometric Methods in Physics | 30.06-6.07.2019 |

VIII School on Geometry and Physics | 24-28.06.2019 |

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## Alexander Turbiner## Choreography in (non)-Newtonian gravityBy definition the choreography (dancing curve) is the trajectory on which n classical bodies move chasing each other without collisions. The first choreography (the remarkable Figure Eight) at zero angular momentum was discovered unexpectedly by C Moore (Santa Fe) at 1993 for 3 equal mass bodies in $\mathbb R^3$ Newtonian gravity numerically. At the moment about 6,000 choreographies are known, all numerically in Newtonian gravity. A number of 3-body choreographies is known for Lenard-Jones potential again numerically; it is proved their existence for quarkonium potential. Do exist (non)-Newtonian gravity for which dancing curve is known analytically? - Yes, one example is known - it is algebraic lemniscate by Jacob Bernoulli (1694) - and it will be the subject of the talk. Astonishingly, Newtonian Figure Eight coincides with algebraic lemniscate with accuracy $10^{-7}$. |

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University of Bialystok |

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