Simanyi N.
The Characteristic Exponents of the Falling Ball Model
(206K, POSTSCRIPT)
ABSTRACT. We study the characteristic exponents of the Hamiltonian system of $n$
($\ge 2$) point masses $m_1,\dots,m_n$ freely falling in the vertical half
line $\{q|\, q\ge 0\}$ under constant gravitation and colliding with each
other and the solid floor $q=0$ elastically. This model was introduced and
first studied by M. Wojtkowski. Hereby we prove his conjecture: All relevant
characteristic (Lyapunov) exponents of the above dynamical system are
nonzero, provided that $m_1\ge\dots\ge m_n$ (i. e. the masses do not increase
as we go up) and $m_1\ne m_2$.