Stability of equilibrium solutions of Hamiltonian systems under the presence of a single resonance in the non-diagonalizable case

DOI10.1134/S1560354708030039zbMath1229.70060OpenAlexW1986778569MaRDI QIDQ652955

Claudio Vidal, Fabio dos Santos

Publication date: 6 January 2012

Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1560354708030039

zbMATH Keywords

stabilitynormal formresonancesHamiltonian system

Mathematics Subject Classification ID

Stability of solutions to ordinary differential equations (34D20) Stability problems for problems in Hamiltonian and Lagrangian mechanics (70H14)

Related Items

Transcendental case in stability problem of Hamiltonian system with two degrees of freedom in presence of first order resonance ⋮ Nonlinear stability of elliptic equilibria in Hamiltonian systems with resonances of order four with interactions ⋮ Stability of equilibrium solutions of Hamiltonian systems with \(n\)-degrees of freedom and single resonance in the critical case ⋮ Instability of equilibrium solutions of Hamiltonian systems with \(n\)-degrees of freedom under the existence of a single resonance and an invariant ray ⋮ Stability of equilibrium solutions of autonomous and periodic Hamiltonian systems in the case of multiple resonances

Cites Work

• Unnamed Item
• Unnamed Item
• Stability of Hamiltonian systems with three degrees of freedom and the three body-problem
• Versal normal form of the Hamiltonian function of the restricted problem of three bodies near \({\mathcal L}_ 4\)
• On the stability of Hamiltonian systems in the presence of resonances
• Stability of equilibrium positions of periodic Hamiltonian systems under third and fourth order resonances
• New aspects in the theory of stability of Hamiltonian systems
• Canonical transformations depending on a small parameter
• Introduction to Hamiltonian dynamical systems and the \(N\)-body problem

This page was built for publication: Stability of equilibrium solutions of Hamiltonian systems under the presence of a single resonance in the non-diagonalizable case