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Higher order corrections to adiabatic invariants of generalized slow-fast Hamiltonian systems (1305.3974v1)
Published 17 May 2013 in math.DS, math-ph, math.MP, and nlin.SI
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.