| Abstract: |
| We model the interactions of an He atom with a Cu surface by the two degrees of
freedom Hamiltonian
\[
H(x,z,p_x,p_z) = \dfrac1{2m}(p_x^2+p_z^2)+V(x,z),
\]
where $V$ is the corrugated Morse potential, $(x,z)$ are the parallel and vertical
positions of the He atom with respect to the Cu surface and $(p_x,p_z)$ are their conjugate
momenta. This is a simplified model where the motion of the He atom is restricted to a plane.
There is numerical evidence in the literature that chaotic motions appear in some regions of the phase space, associated
to motions where the He atom arrives to an infinite height with zero velocity.
In this work we prove that the numerically observed chaotic phenomena do exist in this model.
In particular, we prove the existence of a horseshoe of infinite symbols which, besides chaotic
motions, provides the existence of oscillatory ones, that is, motions in which the He atom arrives to
a higher and higher height, but always returns to the Cu surface. |
|