Abstract:
The problem of knowing the stability of one equilibrium solution of an analytic autonomous Hamiltonian system in a neighborhood of the equilibrium point in the case where all eigenvalues are pure imaginary and the matrix of the linearized system is non-diagonalizable is considered.We give information about the stability of the equilibrium solution of Hamiltonian systems with two degrees of freedom in the critical case. We make a partial generalization of the results to Hamiltonian systems with n degrees of freedom, in particular, this generalization includes those in [1].
Keywords:
Hamiltonian system, stability, normal form, resonances.
Citation:
C. Vidal, F. Dos Santos, “Stability of Equilibrium Solutions of Hamiltonian Systems Under the Presence of a Single Resonance in the Non-Diagonalizable Case”, Regul. Chaotic Dyn., 13:3 (2008), 166–177
\Bibitem{VidDos08}
\by C.~Vidal, F.~Dos Santos
\paper Stability of Equilibrium Solutions of Hamiltonian Systems Under the Presence of a Single Resonance in the Non-Diagonalizable Case
\jour Regul. Chaotic Dyn.
\yr 2008
\vol 13
\issue 3
\pages 166--177
\mathnet{http://mi.mathnet.ru/rcd568}
\crossref{https://doi.org/10.1134/S1560354708030039}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2415371}
\zmath{https://zbmath.org/?q=an:1229.70060}
Linking options:
https://www.mathnet.ru/eng/rcd568
https://www.mathnet.ru/eng/rcd/v13/i3/p166
This publication is cited in the following 5 articles:
Citation in format AMSBIB
Contact us: