# On the solvability of Hamilton's equations in Hilbert spaces

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## Abstract

We construct a bounded function $H : l_2\times l_2 \to R$ with continuous Frechet derivative such that for any $q_0\in l_2$ the Cauchy problem $\dot p= - {\partial H\over\partial q}$, $\dot q={\partial H\over\partial p}$, $p(0) = 0$, q(0) = q_0\$ has no solutions in any neighborhood of zero in R.
Original language English 145-154 10 Infinite Dimensional Analysis Quantum Probability and Related Topics 6 Published - 2003