The characteristic exponents of the falling ball model

Academic Article


  • 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 ≠ m2.
  • Authors

    Digital Object Identifier (doi)

    Author List

  • Simányi N
  • Start Page

  • 457
  • End Page

  • 468
  • Volume

  • 182
  • Issue

  • 2