Conditionally-periodic solutions of the Hamiltonian system with multiple resonance

DOI10.1007/BF00117101zbMath0672.70029OpenAlexW1974736231MaRDI QIDQ1120305

M. K. M. Ahmed, M. H. A. Yousef

Publication date: 1988

Published in: Earth, Moon, and Planets (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00117101

zbMATH Keywords

multiple resonanceconditionally periodic solutions of Hamiltonian systemsdeep resonance

Mathematics Subject Classification ID

Hamilton's equations (70H05) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Local and nonlocal bifurcation theory for dynamical systems (37G99) Nonlinear resonances for nonlinear problems in mechanics (70K30)

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Cites Work

• Construction of conditionally-periodic solutions of canonical systems of differential equations with multiple resonance
• A comparison of the Bohlin-von Zeipel and Bohlin-Lie series methods in resonant systems
• Conditionally periodic solutions of the canonical systems of differential equations in non-autonomous resonant case
• Canonical transformations depending on a small parameter
• Expansion formulae in canonical transformations depending on a small parameter
• Regularization in the Ideal Resonance Problem