Estimation of Rank of Homology Group of Energy Level Surface on Hamiltonian Systems
Qin Tao · Journal of Huaihai Institute of Technology · 2007
This paper intends to make us understand topological structures deeply,and it takes advantage of exact homology sequence and Morse inequalities to estimate the upper bound of the rank of q-dimensional singular homology group of energy level surface(q is an arbitrary nature number).It estimates the ranks of 0-dimension,1-dimension and 2-dimension homology groups,and guesses a formula for the rank of q-dimension singular homology group.It proves that the guess is right and applies it to an example of rigid body dynamics,comparing it with other scholars' conclusions.It succeeds in obtaining a new inequality which estimates the upper bound of the rank of q-dimension singular homology group of energy level surface.