Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.18082 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908979965198336 |
|---|---|
| author | Yang, Putian Zhang, Shiqing |
| author_facet | Yang, Putian Zhang, Shiqing |
| contents | For the Newtonian \(N\)-body problem at nonnegative energy, we study solution sets selected by the Jacobi--Maupertuis variational principle and by the associated stationary Hamilton--Jacobi equation. We prove a compactness/stability theorem for classical initial data generating geodesic rays: limits in the ambient phase space remain collision-free, generate geodesic rays, and carry locally relatively compact normalized Busemann functions. The limiting horofunction of normalized Busemann functions yields a viscosity solution of the limiting stationary equation. For a fixed collision-free hyperbolic limit shape \(a\), we also prove closedness of the corresponding slice of geodesic-ray data. Finally, after passing
to the reduced configuration space \(X\), we show that this fixed-shape slice is countably \(d(N-1)\)-rectifiable in phase space and has Hausdorff dimension exactly \(d(N-1)\). Thus the paper combines phase-space compactness of calibrated minimizing motions with a geometric-measure description of a fixed-shape Hamilton--Jacobi calibrated slice. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_18082 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stability of geodesic-ray data, horofunctions, and rectifiability of fixed-shape slices in the Newtonian \(N\)-body problem Yang, Putian Zhang, Shiqing Analysis of PDEs For the Newtonian \(N\)-body problem at nonnegative energy, we study solution sets selected by the Jacobi--Maupertuis variational principle and by the associated stationary Hamilton--Jacobi equation. We prove a compactness/stability theorem for classical initial data generating geodesic rays: limits in the ambient phase space remain collision-free, generate geodesic rays, and carry locally relatively compact normalized Busemann functions. The limiting horofunction of normalized Busemann functions yields a viscosity solution of the limiting stationary equation. For a fixed collision-free hyperbolic limit shape \(a\), we also prove closedness of the corresponding slice of geodesic-ray data. Finally, after passing to the reduced configuration space \(X\), we show that this fixed-shape slice is countably \(d(N-1)\)-rectifiable in phase space and has Hausdorff dimension exactly \(d(N-1)\). Thus the paper combines phase-space compactness of calibrated minimizing motions with a geometric-measure description of a fixed-shape Hamilton--Jacobi calibrated slice. |
| title | Stability of geodesic-ray data, horofunctions, and rectifiability of fixed-shape slices in the Newtonian \(N\)-body problem |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2604.18082 |