This article is cited in 2 papers

On the Convergence of Coordinate Transformations in the KAM Procedure

M. B. Sevryuk

Institute of Energy Problems of Chemical Physics, The Russian Academy of Sciences, Lenin prospect 38, Bldg. 2, 117829, Moscow, Russia

Abstract: We study the $C^r$-convergence of the compositions $W_n = U_1 U_2 \cdots U_n$ where mappings $U_k$ tend to the identity transformation in the $C^r$-topology as $k \to \infty$. The cases $r = 0$ and $1 \geqslant r < +\infty$ turn out to be drastically different.

MSC: 26B05, 26B40, 34C50

Received: 25.08.1999

Language: English

DOI: 10.1070/RD2000v005n02ABEH000140

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