Thiago Dias

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20152026

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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 $n$ -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 $R^{d}$ , there are $d$ bodies with unit masses at the vertices of a regular $(d - 1)$ -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…

math.DS2018

Generic finiteness for a class of symmetric planar central configurations of the six-body problem and the six-vortex problem

Thiago Dias, Bo-Yu Pan

A symmetric planar central configuration of the Newtonian six-body problem $x$ is called cross central configuration if there are precisely four bodies on a symmetry line of $x$ . W…

math.DS2015

New equations for central configurations and generic finiteness

Thiago Dias

We consider the finiteness problem for central configurations of the $n -$ body problem. We prove that, for $n \geq 4$ , there exists a (Zariski) closed subset $B$ in the mass space $\m…