# Unbounded energy growth in a Hamiltonian system

Does there exist an orbit with unbounded velocity in the system $\ddot x = (-1)^{[t]+[x]}$, where $[*]$ denotes the integer part of *?

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The question seems a bit isolated from context or motivation (and quite specialized, though feel free to correct me if I'm misjudging). Could you please say a bit more about why you want to know? –  Yemon Choi Feb 5 '10 at 18:07
This is one of the simplest time-dependent systems where an orbit with unbounded velocity could conceivably occur, but doesn't obviously occur or not. –  Douglas Zare Feb 6 '10 at 10:30
Yes, I expect that there is an orbit with unbounded velocity but I do not know how to prove it. It is indeed one of the simplest "natural" Hamiltonian systems where KAM does not apply, but on the other hand,there is no obvious way to show nonexistence of invariant curves. There might be some techniques that I am not aware of. –  Vadim Feb 6 '10 at 15:53