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Fachbereich Mathematik Universitat Mainz
Addendum to "Invariant tori in non-degenerate nearly integrable Hamiltonian systems", RCD 6(2) 2001
2005, vol. 10, no. 1, pp. 21-31
For the convenience of the reader of our above mentioned paper we prove here the theorem on the approximation of periodic holomorphic functions by trigonometric polynomials in that paper without any reference to approximation theory, especially to Akhiezer's theorem. See the footnote on p. 136 in RCD 6(2) 2001.
Invariant Tori in Non-Degenerate Nearly Integrable Hamiltonian Systems
2001, vol. 6, no. 2, pp. 119-204
Invariant tori for analytic nearly integrable Hamiltonian systems are constructed under rather weak sufficient conditions being even necessary in the case of maximal invariant tori. All small devisors are controlled by a general approximation function the properties of which correspond to the Bruno condition in analytic problems near a singular point. The admitted size of the perturbations is numerically determined in numerically given systems.