Year: 2025
Type: article
Abstract: We present a new approach for proving that, for a given n, there are finitely many equivalence classes of planar central configurations in the Newtonian n-body problem for generic masses. The human part of the proof relies on tropical geometry. The crux of our technique is in a computation that we have completed for n<=5, thus confirming the celebrated result of Albouy and Kaloshin.
Authors: Anders Jensen, Anton Leykin
Institutions: Aarhus University, Georgia Institute of Technology
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Funder: National Science Foundation
OpenAlex ID: W4413853949