Normal Forms for Lie Symmetric Cotangent Bundle Systems with Free and Proper Actions

DOI10.1007/978-1-4939-2441-7_17zbMath1367.70051arXiv1311.7447OpenAlexW2178346098MaRDI QIDQ3463525

Tanya Schmah, Cristina Stoica

Publication date: 19 January 2016

Published in: Geometry, Mechanics, and Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1311.7447

Mathematics Subject Classification ID

Symmetries, Lie group and Lie algebra methods for problems in mechanics (70G65) Normal forms for nonlinear problems in mechanics (70K45)

Cites Work

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• On the existence of slices for actions of non-compact Lie groups
• A cotangent bundle slice theorem
• Relative equilibria in Hamiltonian systems: The dynamic interpretation of nonlinear stability on a reduced phase space
• Relative equilibria of molecules
• Nekhoroshev-stability of elliptic equilibria of Hamiltonian systems
• Proper group actions and symplectic stratified spaces
• Momentum maps and Hamiltonian reduction
• Hamiltonian systems near relative equilibria
• Long term stability of proper rotations of the perturbed Euler rigid body
• Stability of relative equilibria. I: The reduced energy-momentum method
• Cotangent bundle reduction and Poincaré-Birkhoff normal forms
• Relative equilibria in systems with configuration space isotropy
• Phase space structures governing reaction dynamics in rotating molecules
• Normal form theory for relative equilibria and relative periodic solutions
• AN EXPONENTIAL ESTIMATE OF THE TIME OF STABILITY OF NEARLY-INTEGRABLE HAMILTONIAN SYSTEMS
• Nonlinear stability around an elliptic equilibrium point in a Hamiltonian system

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