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Statistical properties of discretizations of a class of chaotic dynamical systems. (English) Zbl 0854.34043

Summary: Computer simulations of dynamical systems contain discretizations, where finite machine arithmetic replaces continuum state spaces. In some circumstances, complicated theoretical behavior has a tendency to collapse to trivial and degenerate behavior as a result of discretizations. Various statistical estimators associated with such collapsing effects often seem to depend on the corresponding discretization in a random way. Behavior of some statistical properties of the collapse is discussed. Results of computer modeling of mappings \(x\mapsto 1- |1- 2x|^\ell\), \(x\in [0, 1]\), \(\ell> 2\) are presented.

MSC:

34C28 Complex behavior and chaotic systems of ordinary differential equations
37-XX Dynamical systems and ergodic theory
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