Morse Thoery of Saddle Point Reduction with Applications

Abstract

In this paper, we demonstrate that when saddle point reduction is applicable, there is a clear relationship between the Morse index and the critical groups before and after the reduction. As an application of this result, we use saddle point reduction along with the critical point theorem to show the existence of periodic solutions in second-order Hamiltonian systems.

Keywords

• Morse index
• critical group
• Morse theory
• critical point theorem
• saddle point reduction
• Hamiltonian systems