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Interval stochastic matrices and simulation of chaotic dynamics. (English) Zbl 0811.58042

Kloeden, Peter E. (ed.) et al., Chaotic numerics. An international workshop on the approximation and computation of complicated dynamical behavior, July 12-16, 1993, Deakin Univ., Geelong, Australia. Providence, RI: American Mathematical Society. Contemp. Math. 172, 203-215 (1994).
The relationship between a chaotic dynamical system and approximate spatial discretizations appropriate for computer simulation is analyzed. The discretization amounts to perturbations which may cause most intricate attractors and completely mixing invariant measures to collapse into, say, a single fixed point and its corresponding atomic measure.
The paper analyzes the nature of collapsing effects (sufficient conditions for collapse to occur), and discusses strategies allowing to avoid them. As a new tool, the interval stochastic matrices and multi- valued discretizations are introduced.
Subsequently, the level of “multiwavedness” and/or the minimal level of stochasticity sufficient to suppress collapsing effects, are studied.
For the entire collection see [Zbl 0801.00025].

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
65G30 Interval and finite arithmetic
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