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2013
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# Joachim Albrecht

Friedrichshof, 50997 Köln

## Publications:

 Albrecht J. On the Existence of Invariant Tori in Nearly-Integrable Hamiltonian Systems With Finitely Differentiable Perturbations 2007, vol. 12, no. 3, pp.  281-320 Abstract We prove the existence of invariant tori in Hamiltonian systems, which are analytic and integrable except a $2n$-times continuously differentiable perturbation ($n$ denotes the number of the degrees of freedom), provided that the moduli of continuity of the $2n$-th partial derivatives of the perturbation satisfy a condition of finiteness (condition on an integral), which is more general than a Hölder condition. So far the existence of invariant tori could be proven only under the condition that the $2n$-th partial derivatives of the perturbation are Hölder continuous. Keywords: nearly integrable Hamiltonian systems, KAM theory, perturbations, small divisors, Celestial Mechanics, quasi-periodic motions, invariant tori, trigonometric approximation in several variables, Holder condition Citation: Albrecht J.,  On the Existence of Invariant Tori in Nearly-Integrable Hamiltonian Systems With Finitely Differentiable Perturbations, Regular and Chaotic Dynamics, 2007, vol. 12, no. 3, pp. 281-320 DOI:10.1134/S1560354707030033