Abstract
The purpose of this paper is to prove an extension of the local version of Kolmogorov’s theorem on the invariance of quasiperiodic motions under small pertubations of the Hamiltonian. However, this proof serves only as an example in order to demonstrate a new calculus of estimates which differs from the one of Arnol’d [2] and Moser [7] in so far as rapid convergence of the iteration process does not take place. In fact, in conjugacy problems without small divisors our approach coincides with the ordinary Lipschitz iteration. On the other hand, the utmost of possible influence of the small divisors is admitted.
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Rüssmann, H. (1994). On the Frequencies of Quasi Periodic Solutions of Analytic Nearly Integrable Hamiltonian Systems. In: Kuksin, S., Lazutkin, V., Pöschel, J. (eds) Seminar on Dynamical Systems. Progress in Nonlinear Differential Equations and Their Applications, vol 12. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7515-8_13
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DOI: https://doi.org/10.1007/978-3-0348-7515-8_13
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