Central Configurations of the N-body problem.<br/><br/>
Friday, July 1, 2011 - 11:20am - 11:50am
I recently discovered a new phenomenon on central configurations in the collinear three-body problem and in the collinear four-body problem. There exists a configuration that is a central configuration for at least two different arrangements of a given mass vector. Such central configuration is called the super central configuration in the $n$-body problem and it may lead some surprising dynamical behaviors. Super central configurations do not exist in the planar four-body problem. The existence and classifications of super central configuration in the collinear cases are also very important for counting the number of central configurations under different equivalent classes. When I extend to study the super central configurations in general homogeneous potential, the existence of super central configurations has a relation to the Mathematical Beatuy- Golden Ratio.