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Models of knowing and the investigation of dynamical systems. (English) Zbl 0940.37021
The authors identify three distinct paradigms (models of knowing) for scientific understanding of dynamical systems. According to the first of them a dynamical system is understood by modeling it with a differential equation and then solving this equation. The second one is the qualitative theory which also based on differential equations but gives the qualitative information about the system’s behaviour without solving the corresponding equations. The third one is the so called algorithmic modeling paradigm where both the dynamical system and its solutions are approximated algorithmically (usually with the aid of computers).
The authors give a short historical review for each of these paradigms, describe their advantages and disadvantages and indicate the possible ways of further development for the most recent paradigm of algorithmic modeling.

MSC:
37J05 Relations of dynamical systems with symplectic geometry and topology (MSC2010)
37F05 Dynamical systems involving relations and correspondences in one complex variable
37M99 Approximation methods and numerical treatment of dynamical systems
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