BASIN OF ATTRACTION OF CYCLES OF DISCRETIZATIONS OF DYNAMICAL-SYSTEMSWITH SRB INVARIANT-MEASURES

Computer simulations of dynamical systems are discretizations, where t he finite space of machine arithmetic replaces continuum state spaces. So any trajectory of a discretized dynamical system is eventually per iodic. Consequently, the dynamics of such computations are essentially determined by the cycles of the discretized map. This paper examines the statistical properties of the event that two trajectories generate the same cycle. Under the assumption that the original system has a S inai-Ruelle-Bowen invariant measure, the statistics of the computed ma pping are shown to be very close to those generated by a class of rand om graphs. Theoretical properties of this model successfully predict t he outcome of computational experiments with the implemented dynamical systems.