3 problems

Consider planar equilateral 5-body central configurations with all masses positive in the Newtonian case. The regular pentagon and the star are the configurations with equal masses…

Let the five masses be nonzero, and suppose the potential exponent is a real number $A\geq 2$. A planar equilateral 5-body central configuration is a central configuration of five…

Let $f$ be the function for the equal-mass planar five-body problem, let $\mathcal{C}_5$ be the quotient configuration space, and let $P(t)$ be its Poincaré polynomial. Five-body M…