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Collapsing effects in numerical simulation of a class of chaotic dynamical systems and random mappings with a single attracting centre. (English) Zbl 0878.60094

Summary: Computer simulations of dynamical systems contain discretizations, where finite machine arithmetic replaces continuum state spaces. In some circumstances, complicated theoretical behaviour has a tendency to collapse to trivial and degenerate behaviour as a result of discretizations. Characteristics of such collapsing effects often seem to depend on the corresponding discretization only in a random say. We describe a procedure to construct a stochastic process with similar statistical characteristics. Results of computer modelling are discussed.

MSC:

60K99 Special processes
37E99 Low-dimensional dynamical systems
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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