Instability and bifurcation near the symplectic 1 :4 resonance

DOI10.1080/02681119708806248zbMath0926.70022OpenAlexW1984205165MaRDI QIDQ4237736

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Publication date: 21 November 1999

Published in: Dynamics and Stability of Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/02681119708806248

zbMATH Keywords

linearizationconfiguration spacePoincaré sectioniterated symplectic mapspinning double-orthogonal pendulumtruncated normal formtwo-parameter family of symplectic maps

Mathematics Subject Classification ID

Stability problems for problems in Hamiltonian and Lagrangian mechanics (70H14)

Related Items (4)

Fourth order resonant collisions of multipliers in reversible maps: period-4 orbits and invariant curves ⋮ A transverse spinning double pendulum ⋮ Resonant collisions in four-dimensional reversible maps: a description of scenarios ⋮ Quasi-periodic stability of normally resonant tori

Cites Work

• Periodic orbits for reversible, symplectic mappings
• Homoclinic orbits in Hamiltonian systems
• Dynamics of a parametrically excited double pendulum
• Unipotent normal forms for symplectic maps
• Fourth order resonant collisions of multipliers in reversible maps: period-4 orbits and invariant curves
• Bifurcation of periodic solutions near a collision of eigenvalues of opposite signature
• Converse KAM theory for symplectic twist maps
• Symplectic maps, variational principles, and transport
• Bifurcation sequences at 1:4 resonance: an inventory
• On the Normal Forms of Linear Canonical Transformations in Dynamics

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