Adiabatic invariants for linear Hamiltonian systems |
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Authors: | Anthony Leung Kenneth Meyer |
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Affiliation: | Department of Mathematics, University of Cincinnati, Cincinnati, Ohio 45221 U.S.A. |
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Abstract: | n independent adiabatic invariants in involution are found for a slowly varying Hamiltonian system of order 2n × 2n. The Hamiltonian system considered is , where A(t) is a 2n × 2n real matrix with distinct, pure imaginary eigen values for each t? [?∞, ∞], and , for all j > 0. The adiabatic invariants Is(u, t), s = 1,…, n are expressed in terms of the eigen vectors of A(t). Approximate solutions for the system to arbitrary order of ? are obtained uniformly for t? [?∞, ∞]. |
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