2013/05/14 by Alain Albouy, Hildeberto E. Cabral, Alan A. Santos · 1 citation
Physics and Astronomy · Mathematics · #math-ph #math.DS #math.MP #msc:70F10 #msc:70F15
paper · pdf · doi:10.1007/s10569-012-9431-1
published as Celestial Mechanics and Dynamical Astronomy, 113(4) (2012), pp. 369-375 · 10 pages, list of mathematical problems
arxiv created 2013/05/14 · arxiv updated 2013/05/15
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.