Higher order corrections to adiabatic invariants of generalized slow-fast Hamiltonian systems

Abstract

We present a coordinate-free approach for constructing approximate first integrals of generalized slow-fast Hamiltonian systems, based on the global averaging method on parameter-dependent phase spaces with ${\mathbb{S}}^1-$symmetry. Explicit global formulas for approximate second-order first integrals are derived. As examples, we analyze the case quadratic in the fast variables (in particular, the elastic pendulum), and the charged particle in a slowly-varying magnetic field.

First version

References in corpus (1)

• Homological Equation for Tensor Field and Periodic Averaging

Cited by in corpus (3)

• Invariant Poisson Realizations and the Averaging of Dirac Structures
• Adiabatics using quantum action
• A geometric proof of the periodic averaging theorem on Riemannian manifolds