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- W2004927227 abstract "We give a mechanical example concerning the fact that some regularity is necessary in KAM theory. We consider the model given by the vertical bouncing motion of a ball on a periodically moving plate. Denoting with $f$ the motion of the plate, some variants of Moser invariant curve theorem apply if $dot{f}$ is small in norm $C^5$ and every motion has bounded velocity. This is not possible if the function $f$ is only $C^1$. Indeed we construct a function $fin C^1$ with arbitrary small derivative in norm $C^0$ for which a motion with unbounded velocity exists." @default.
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- W2004927227 date "2014-08-01" @default.
- W2004927227 modified "2023-10-17" @default.
- W2004927227 title "A mechanical counterexample to KAM theory with low regularity" @default.
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- W2004927227 doi "https://doi.org/10.1016/j.physd.2014.05.010" @default.
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