Abstract
This paper concerns with the study of the stability of one equilibrium solution of an autonomous analytic Hamiltonian system in a neighborhood of the equilibrium point with 1-degree of freedom in the degenerate case H = q4 + H5 + H6 +.... Our main results complement the study initiated by Markeev in [9].
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Gutierrez, R., Vidal, C. Stability of Equilibrium Points for a Hamiltonian Systems with One Degree of Freedom in One Degenerate Case. Regul. Chaot. Dyn. 22, 880–892 (2017). https://doi.org/10.1134/S1560354717070097
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DOI: https://doi.org/10.1134/S1560354717070097
Keywords
- Hamiltonian system
- equilibrium solution
- type of stability
- normal form
- critical cases
- Lyapunov’s Theorem
- Chetaev’s Theorem