Minimizing methods have been successfully applied to construct various types of periodic solutions for the n-body and n-center problems during the past two decades. Majority of relevant researches were endeavored to understand qualitative features such as existence, uniqueness, and stability. In this talk we discuss a topic with relatively less attention — quantitative estimates for action values and mutual distances for action minimizing solutions. We will demonstrate some simple but nontrivial bounds. These estimates will facilitate numerical explorations to effectively locate and search new orbits.
A. Albouy, A. Chenciner, J. Laskar
