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Regular version of the site

Article

Inserted perturbations generating asymptotical integrability

Mathematical notes. 2014. Vol. 96. No. 6. P. 965-970.

We discuss the general opportunity to create (asymptotically) a comletely integrable system from the original perturbed system by inserting additional perturbing terms. After such an artificial insertion,  there appears an opportunity to make the secondary averaging and secondary reduction of the original system. Thus, by this way, the $3D$-system becomes $1$-dimensional. We demonstrate this approach by the example of a resonance Penning trap.