The Characteristic Exponents of the Falling Ball Model
The Characteristic Exponents of the Falling Ball Model
N. Simányi
The Characteristic Exponents of the Falling Ball Model
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 $m_1\ne m_2$.