3 papers
math.DS2026
Brehm-Wintner-Conley Dimension, Plücker Coordinates, and Generalized Dziobek-Williams Equations for Central Configurations
Thiago Dias
We develop an algebraic framework for central configurations of the -body problem with homogeneous potentials, grounded in the exterior algebra of the configuration space and th…
math.DS2026
Generalized Laura-Andoyer equations and the enumeration of some symmetrical classes of Dziobek configurations
Thiago Dias, Ya-Lun Tsai
We study the symmetrical Dziobek configurations where, in , there are bodies with unit masses at the vertices of a regular -dimensional simplex of unit e…
math.DS2026
The Veronese Geometry of Dziobek Configurations and Generic Finiteness for Homogeneous Potentials
Thiago Dias
The main contribution of this paper is the proof of the generic finiteness of Dziobek central configurations for a homogeneous potential and the derivation of a uniform upper bound…