The characteristic exponents of the falling ball model

We study the characteristic exponents of the Hamiltonian system ofn (>=2) point massesm ₁,...,m _n freely falling in the vertical half line {q|q>=0} under constant gravitation and colliding with each other and the solid floorq=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 thatm ₁>= ...>=m _n (i.e. the masses do not increase as we go up) andm ₁≠m ₂. Research partially supported by the Hungarian National Foundation for Scientific Research, No. 16425.