Date of Award
8-2025
Degree Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
School
Mathematics and Natural Sciences
Committee Chair
Dr. Zhifu Xie
Committee Chair School
Mathematics and Natural Sciences
Committee Member 2
Dr. Jiu Ding
Committee Member 2 School
Mathematics and Natural Sciences
Committee Member 3
Dr. Qingguang Guan
Committee Member 3 School
Mathematics and Natural Sciences
Committee Member 4
Dr. James V. Lambers
Committee Member 4 School
Mathematics and Natural Sciences
Committee Member 5
Dr. Haiyan Tian
Committee Member 5 School
Mathematics and Natural Sciences
Committee Member 6
Dr. Huiqing Zhu
Committee Member 6 School
Mathematics and Natural Sciences
Abstract
In the study of central configurations of the N-body problem, degeneracy plays a significant role---whether in thoroughly understanding bifurcation theory or in counting the number of central configurations to attempt a proof of the famous Chazy-Wintner-Smale conjecture. This dissertation is devoted to developing a new practical algorithm for determining the nondegeneracy of a given collision-free central configuration. Two key theorems are established to identify trivial zero eigenvalues of the Jacobian matrix, enabling the implementation of the algorithm. Subsequently, this criterion is applied to demonstrate the nondegeneracy of collision-free restricted central configuration problems. As a concrete application, the collision-free (3+L)-body central configurations are proved to be nondegenerate.
Copyright
Xiaodong Wang, 2025
Recommended Citation
Wang, Xiaodong, "On the Degeneracy of Central Configurations" (2025). Dissertations. 2382.
https://aquila.usm.edu/dissertations/2382