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Mat. Zametki, 2004, Volume 76, Issue 5, Pages 701–713 (Mi mz140)  

Normal Forms near Two-Dimensional Resonance Tori for the Multidimensional Anharmonic Oscillator

S. Yu. Dobrokhotov, M. A. Poteryakhin

A. Ishlinsky Institite for Problems in Mechanics, Russian Academy of Sciences

Abstract: 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.

DOI: https://doi.org/10.4213/mzm140

Full text: PDF file (588 kB)
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English version:
Mathematical Notes, 2004, 76:5, 653–664

Bibliographic databases:

UDC: 517.958
Received: 25.09.2003

Citation: S. Yu. Dobrokhotov, M. A. Poteryakhin, “Normal Forms near Two-Dimensional Resonance Tori for the Multidimensional Anharmonic Oscillator”, Mat. Zametki, 76:5 (2004), 701–713; Math. Notes, 76:5 (2004), 653–664

Citation in format AMSBIB
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