2023/07/01 by Vladimir Zolotov, Zolotov, Vladimir · 1 citation
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #31B05 #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #Classical Analysis and ODEs (math.CA) #Defense, Military, and Policy Studies #FOS: Mathematics #FOS: Physical sciences #Mathematical Approximation and Integration #Mathematical Physics (math-ph) #Nuclear physics research studies
paper · pdf · doi:10.48550/arxiv.2307.00312
openalex publication_date 2023/07/01 · openalex created_date 2023/07/05 · openalex updated_date 2026/07/28
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 n-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.