Chaotic dynamics of a bouncing ball (Q1079254)

A mapping of a half cylinder \(R^+_ 0\times S^ 1\) onto itself is examined, which is framed in terms of a pair of difference equations: \[ v_{n+1}=\epsilon v_ n+(1+\epsilon)(1+\sin \vartheta_ n), \] \[ \vartheta_{n+1}=\vartheta_ n+Bv_{n+1}mod 2\pi. \] The evolution of the attracting set with changing parameter and the behaviour of Lyapunov exponents in the quasiperiodic regime under the influence of external noise are discussed.