@article{Żoła̧dek2024, 
author = {Henryk Żoła̧dek},
title = {An example in Hamiltonian dynamics},
year = {2024},
journal = {Communications in Analysis and Mechanics},
volume = {16},
number = {2},
pages = {431-447},
keywords = {Hamiltonian system, periodic solutions, Lyapunov theorem},
url = {https://www.sciopen.com/article/10.3934/cam.2024020},
doi = {10.3934/cam.2024020},
abstract = {We present an example of a three-degrees-of-freedom polynomial Hamilton function with a critical point characterized by indefinite quadratic part with a Morse index 2. This function generates a Hamiltonian system wherein all eigenvalues equal  ±i, but it lacks small-amplitude periodic solutions with a period  ≈2π.}
}