Geodesic
Normal Forms near Two-Dimensional Resonance Tori for the Multidimensional Anharmonic Oscillator
Matematičeskie zametki, Tome 76 (2004) no. 5, pp. 701-713 
S. Yu. Dobrokhotov; M. A. Poteryakhin. Normal Forms near Two-Dimensional Resonance Tori for the Multidimensional Anharmonic Oscillator. Matematičeskie zametki, Tome 76 (2004) no. 5, pp. 701-713. http://geodesic.mathdoc.fr/item/MZM_2004_76_5_a5/
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     author = {S. Yu. Dobrokhotov and M. A. Poteryakhin},
     title = {Normal {Forms} near {Two-Dimensional} {Resonance} {Tori} for the {Multidimensional} {Anharmonic} {Oscillator}},
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Voir la notice de l'article provenant de la source Math-Net.Ru

We study the problem of constructing a normal form near a two-dimensional invariant isotropic torus for a multidimensional anharmonic oscillator. We construct a fourth-order normal form with respect to harmonic oscillator type variables. We show that, in the presence of resonances, the dependence of the normal form on the action type variables becomes nonpolynomial.

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