Some Problems on the Classical N-Body Problem

Abstract

Our idea is to imitate Smale's list of problems, in a restricted domain of mathematical aspects of Celestial Mechanics. All the problems are on the n-body problem, some with different homogeneity of the potential, addressing many aspects such as central configurations, stability of relative equilibrium, singularities, integral manifolds, etc. Following Steve Smale in his list, the criteria for our selection are: (1) Simple statement. Also preferably mathematically precise, and best even with a yes or no answer. (2) Personal acquaintance with the problem, having found it not easy. (3) A belief that the question, its solution, partial results or even attempts at its solution are likely to have great importance for the development of the mathematical aspects of Celestial Mechanics.

10 pages, list of mathematical problems

Cited by in corpus (16)

• Relative Equilibria in the Four-Vortex Problem with Two Pairs of Equal Vorticities
• A Four-Body Convex Central Configuration with Perpendicular Diagonals Is Necessarily a Kite
• Collision index and stability of elliptic relative equilibria in planar n-body problem
• On the uniqueness of trapezoidal four-body central configurations
• Bifurcations of Central Configurations in the Four-Body Problem with some equal masses
• Classifying Four-Body Convex Central Configurations
• On the Uniqueness of Co-circular Four Body Central Configurations
• Linear stability of the elliptic relative equilibrium with $(1+n)$-gon central configurations in planar $n$-body problem
• Existence of a lower bound for the distance between point masses of relative equilibria for generalised quasi-homogeneous $n$-body problems and the curved $n$-body problem
• Periodic orbits for 3 and 4 co-orbital bodies
• Existence, stability, and symmetry of relative equilibria with a dominant vortex
• Linear stability of elliptic relative equilibria of four-body problem with two infinitesimal masses
• On the sectional curvature along central configurations
• Decomposition of Symmetrical Classes of Central Configurations
• A limit of nonplanar 5-body central configurations is nonplanar
• A natural decomposition of the Jacobi equation for some classes of $N$-body problems