arXiv subjects
Publications and source records attributed to Henrik Schließauf.
We study the one-dimensional Fermi-Ulam ping-pong problem with a Bohr almost periodic forcing function and show that the set of initial condition leading to escaping orbits typically has Lebesgue measure zero.
We study the superlinear oscillator equation $\ddot{x}+ \lvert x \rvert^{α-1}x = p(t)$ for $α\geq 3$, where $p$ is a quasi-periodic forcing with no Diophantine condition on the frequencies and show that typically the set of initial values leading to solutions $x$ such that $\lim_{t\to\infty} (\lvert x(t) \rvert + \lvert \dot{x}(t) \rvert) = \infty$ has Lebesgue measure zero, provided the starting energy $\lvert x(t_0) \rvert + \lvert \dot{x}(t_0) \rvert$ is sufficiently large.