Kustaanheimo–Stiefel correspondence for spatial perturbed Kepler problems

Establish the spatial Kustaanheimo–Stiefel analogue of the planar correspondence between generalized periodic solutions produced by a Lusternik–Schnirelmann argument for a periodically perturbed Kepler problem and solutions represented by regularized variables.

Background

The paper compares its collision-free, locally continued solutions with the global topological approach of Boscaggin, Ortega, and Zhao for small time-periodic perturbations of the Kepler problem. In the planar case, the generalized periodic solutions obtained by that approach can be identified with solutions arising from Levi–Civita regularization. The analogous identification in three dimensions, using Kustaanheimo–Stiefel variables, is explicitly left unresolved.

References

In the plane they are identified with the solutions given by the Levi-Civita regularization, whereas in space the corresponding statement for the Kustaanheimo--Stiefel variables is left open there.

— Platonic constellations of periodic motions in the $(n + 1)$-body problem  (2609.10242 - Constantineau et al., 9 Sep 2026) in Introduction, paragraph “Relation to the global methods”