Upper bounds for the number of isolated critical points via Thom-Milnor theorem
Mathematical Physics
2023-07-18 v2 Algebraic Geometry
Algebraic Topology
Classical Analysis and ODEs
math.MP
Abstract
We apply the Thom-Milnor theorem to obtain the upper bounds on the amount of isolated (1) critical points of a potential generated by several fixed point charges(Maxwell's problem on point charges), (2) critical points of SINR, (3) critical points of a potential generated by several fixed Newtonian point masses augmented with a quadratic term, (4) central configurations in the -body problem. In particular, we get an exponential bound for Maxwell's problem and the polynomial bound for the case of an "even dimensional" potential in Maxwell's problem.
Keywords
Cite
@article{arxiv.2307.00312,
title = {Upper bounds for the number of isolated critical points via Thom-Milnor theorem},
author = {Vladimir Zolotov},
journal= {arXiv preprint arXiv:2307.00312},
year = {2023}
}
Comments
A reference to Kuzmina's work is added. The work has a very similar bound for the number of central configurations