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Hamiltonian systems with linear normal form near an invariant torus. (English) Zbl 0744.58019

Nonlinear dynamics, Proc. Conf., Bologna/Italy 1988, 11-29 (1989).
[For the entire collection see Zbl 0741.00081.]
The author gives a new proof of a theorem of Rüssmann on Hamiltonian systems with linear normal forms by generalizing Siegel’s method for estimates of small divisors. His approach also gives an answer to a problem posed by Gallavotti.

MSC:

37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
37G05 Normal forms for dynamical systems

Citations:

Zbl 0741.00081
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