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2013
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# Helmut Russmann

Staudingerweg 9, D-55099 Mainz, Germany
Fachbereich Mathematik Universitat Mainz

## Publications:

 Russmann H. Addendum to "Invariant tori in non-degenerate nearly integrable Hamiltonian systems", RCD 6(2) 2001 2005, vol. 10, no. 1, pp.  21-31 Abstract 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. Keywords: good approximation of multi-periodic, analytic functions by trigonometric polynomials in a multi-dimensional strip Citation: Russmann H.,  Addendum to "Invariant tori in non-degenerate nearly integrable Hamiltonian systems", RCD 6(2) 2001 , Regular and Chaotic Dynamics, 2005, vol. 10, no. 1, pp. 21-31 DOI: 10.1070/RD2005v010n01ABEH000297
 Russmann H. Invariant Tori in Non-Degenerate Nearly Integrable Hamiltonian Systems 2001, vol. 6, no. 2, pp.  119-204 Abstract 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. Citation: Russmann H.,  Invariant Tori in Non-Degenerate Nearly Integrable Hamiltonian Systems, Regular and Chaotic Dynamics, 2001, vol. 6, no. 2, pp. 119-204 DOI:10.1070/RD2001v006n02ABEH000169