On the accuracy of conservation of adiabatic invariants in slow-fast Hamiltonian systems
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Let the adiabatic invariant of action variable in a slow-fast Hamiltonian system with two degrees of freedom have limits along the trajectories as time tends to plus and minus infinity. The difference of these two limits is exponentially small in analytic systems. An isoenergetic reduction and canonical transformations are applied to transform the slow-fast system to form of a system depending on a slowly varying parameter in a complexified phase space. On the basis of this method an estimate for the accuracy of conservation of adiabatic invariant is given.
Keywordsadiabatic invariant slow-fast Hamiltonian systems isoenergetic reduction
MSC2010 numbers70H11 70K70 34C29
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