On the Global Structure of Normal Forms for Slow-Fast Hamiltonian Systems

2013/02/14 by Vorobiev, M. Avendaño Camacho Yu.
#FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1302.3301

Abstract

In the framework of Lie transform and the global method of averaging, the normal forms of a multidimensional slow-fast Hamiltonian system are studied in the case when the flow of the unperturbed (fast) system is periodic and the induced S¹-action is not necessarily free and trivial. An intrinsic splitting of the second term in a S¹-invariant normal form of first order is derived in terms of the Hannay-Berry connection associated with the periodic flow.

Related

• Slow-fast systems with an equilibrium near the folded slow manifold
• Non Quasi-Periodic Normal Form Theory
• Normalization flow
• Normalization flow in the presence of a resonance
• Averaging, symplectic reduction, and central extensions