Universal dynamics in celestial mechanics
Determine whether celestial-mechanics systems possess universal Poincaré maps: namely, whether, for every symplectic embedding of the disk into and every , there exist a restricted planar circular -body problem, a Poincaré map of that system, and a renormalization such that . The broader problem concerns universality for the relevant class of celestial-mechanics Poincaré maps, beyond the finite-dimensional realization obtained by varying and the masses of the primaries.
References
Primary source
Additional references
- Universal Dynamics in a family of Celestial Mechanics models — arXiv — Miguel Garrido, Pau Martín
Progress summary
A new paper claims a restricted universality result, but the broader celestial-mechanics problem remains open and the claim has not been independently corroborated.
The problem asks whether the specified celestial-mechanics family can realize universal dynamics, including approximation of symplectic disk maps through homoclinic dynamics. Miguel Garrido and Pau Martín claim a finite-dimensional result by varying the number and masses of primaries, which falls short of the full intended universality statement.
October 7, 2026 finite-dimensional universality claim
Garrido and Martín’s paper claims universality for a restricted planar circular many-body family, with the number and masses of primaries serving as parameters. This is substantive claimed progress, not a resolution of the full problem; the retrieved material contains no independent mathematical assessment of the paper.
Current status (as of October 2026): A finite-dimensional weak universality result is claimed for a restricted family, while universality in the full intended celestial-mechanics class remains open and the claim is unverified.
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