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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.14170 |
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| _version_ | 1866909910621487104 |
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| author | Cerritos, Juan Manuel Sánchez |
| author_facet | Cerritos, Juan Manuel Sánchez |
| contents | We prove the existence of planar $D_n$--equivariant choreographies in the $n$--body problem with homogeneous potential of degree $-α$, $0<α<2$. Each body follows the same closed path, rotated and time-shifted, forming a choreography whenever the winding number $W$ is coprime with $n$. Using Mawhin's coincidence degree, we establish collision-free periodic solutions under a simple nonresonance condition. The proof relies on the spectral structure of the linearized operator, symmetry-induced separation of the bodies, and uniform energy bounds ensuring compactness of the nonlinear term. This provides a topological route to choreographies beyond variational and numerical frameworks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_14170 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Choreographies with Dihedral Symmetry in the Planar $n$-Body Problem Cerritos, Juan Manuel Sánchez Dynamical Systems We prove the existence of planar $D_n$--equivariant choreographies in the $n$--body problem with homogeneous potential of degree $-α$, $0<α<2$. Each body follows the same closed path, rotated and time-shifted, forming a choreography whenever the winding number $W$ is coprime with $n$. Using Mawhin's coincidence degree, we establish collision-free periodic solutions under a simple nonresonance condition. The proof relies on the spectral structure of the linearized operator, symmetry-induced separation of the bodies, and uniform energy bounds ensuring compactness of the nonlinear term. This provides a topological route to choreographies beyond variational and numerical frameworks. |
| title | Choreographies with Dihedral Symmetry in the Planar $n$-Body Problem |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2511.14170 |