# The stability of equilibrium solutions of periodic Hamiltonian systems in the case of degeneracy

## TL;DR

This paper investigates the stability of equilibrium solutions in periodic Hamiltonian systems with degeneracy, providing conditions for stability and instability by analyzing high order terms when linearized characteristic exponents are zero.

## Contribution

It introduces new sufficient conditions for stability and instability in degenerate periodic Hamiltonian systems considering high order terms.

## Key findings

- Sufficient conditions for stability identified
- Sufficient conditions for instability identified
- Analysis applicable to almost all degenerate cases

## Abstract

In this paper we are concerned with the stability of equilibrium solutions of periodic Hamiltonian systems with one degree of freedom in the case of degeneracy, which means that the characteristic exponents of the linearized system have zero real part, and the high order terms must be considered to solve the stability problem. For almost all degenerate cases, sufficient conditions for the stability and instability are obtained.