Nonlinear stability of elliptic equilibria in Hamiltonian systems with exponential time estimates

DOI10.3934/dcds.2021073zbMath1479.37060OpenAlexW3159239234WikidataQ115483821 ScholiaQ115483821MaRDI QIDQ1983306

Claudio Vidal, Daniela Cárcamo-Díaz, Patricia Yanguas, Jesús F. Palacián

Publication date: 10 September 2021

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2021073

zbMATH Keywords

resonancesformal stabilityelliptic equilibriaexponential time estimatesLie stability

Mathematics Subject Classification ID

Equilibria and periodic trajectories for nonlinear problems in mechanics (70K42) Stability problems for finite-dimensional Hamiltonian and Lagrangian systems (37J25) Stability problems for problems in Hamiltonian and Lagrangian mechanics (70H14)

Related Items

Nonlinear stability of elliptic equilibria in Hamiltonian systems with resonances of order four with interactions

Cites Work

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• The steep Nekhoroshev's theorem
• Asymptotic stability estimates near an equilibrium point
• Stability of equilibrium solutions of autonomous and periodic Hamiltonian systems with \(n\)-degrees of freedom in the case of single resonance
• Stability of equilibrium solutions of Hamiltonian systems with \(n\)-degrees of freedom and single resonance in the critical case
• The separation of motions in systems with rapidly rotating phase
• Interaction of third-order resonances in problems of the stability of Hamiltonian systems
• Small vibrations of one-dimensional moving bodies
• On the stability of autonomous systems in the presence of several resonances
• Nekhoroshev-stability of elliptic equilibria of Hamiltonian systems
• Nekhoroshev-stability of \(L4\) and \(L5\) in the spatial restricted three-body problem
• Instability of equilibrium solutions of Hamiltonian systems with \(n\)-degrees of freedom under the existence of a single resonance and an invariant ray
• Normally stable Hamiltonian systems
• On the nonlinear stability of the triangular points in the circular spatial restricted three-body problem
• Super-exponential stability for generic real-analytic elliptic equilibrium points
• Stability of equilibrium solutions of autonomous and periodic Hamiltonian systems in the case of multiple resonances
• Higher-order averaging, formal series and numerical integration. III: Error bounds
• Instability of equilibrium solutions of Hamiltonian systems with \(n\)-degrees of freedom under the existence of multiple resonances and an application to the spatial satellite problem
• On the stability of Hamiltonian systems in the presence of resonances
• Über die Existenz einer Normalform analytischer Hamiltonscher Differentialgleichungen in der Nähe einer Gleichgewichtslösung
• New aspects in the theory of stability of Hamiltonian systems
• AN EXPONENTIAL ESTIMATE OF THE TIME OF STABILITY OF NEARLY-INTEGRABLE HAMILTONIAN SYSTEMS
• Nonlinear stability around an elliptic equilibrium point in a Hamiltonian system
• Complex analysis and convolution operators
• Stability of equilibria and fixed points of conservative systems
• Prevalence of exponential stability among nearly integrable Hamiltonian systems
• Formal stability of Hamiltonian systems
• On the formulation of new explicit conditions for steepness from a former result of N.N. Nekhoroshev
• Diffusion and stability in perturbed non-convex integrable systems
• Introduction to Hamiltonian dynamical systems and the \(N\)-body problem