A pr 1 99 6 March 8 , 1996 The Characteristic Exponents of the Falling Ball Model

We study the characteristic exponents of the Hamiltonian system of n (≥ 2) point masses m1, . . . , mn freely falling in the vertical half line {q| q ≥ 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 m1 ≥ · · · ≥ mn (i. e. the masses do not increase as we go up) and m1 6= m2.