Abstract
1. Let a dynamic system depend on the slowly varying parameter λ = εt; then the Hamiltonian H(p, q; λ) contains the time t and is not conserved. A function J(p, q; λ) is called an adiabatic invariant of the system if for small ε the quantity J(t) = J[p(t), q(t); λ(t)] changes slightly during the time t ~ 1/ε (changes in λ, H are finite here).
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(2009). On the behavior of an adiabatic invariant under slow periodic variation of the Hamiltonian. In: Givental, A., et al. Collected Works. Vladimir I. Arnold - Collected Works, vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01742-1_16
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DOI: https://doi.org/10.1007/978-3-642-01742-1_16
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