A MODEL FOR ROUNDOFF AND COLLAPSE IN COMPUTATION OF CHAOTIC DYNAMICAL-SYSTEMS

Computer simulations of dynamical systems contain discretizations, whe re finite machine arithmetic replaces continuum state space. For chaot ic dynamical systems, the main features of this discretization are sto chastically related to the parameters both, of the underlying continuo us system and of the computer arithmetic. A model of this process is r equired to describe and analyze its statistical properties and this is carried out for the family of mappings f(l)(x) = 1 - \1 - 2x\(l), x i s an element of [0, 1], l > 2. Computer modeling results are presented .