On extracting physical information from mathematical models of chaotic and complex systems

The paper describes a multi-structural approach to the problem indicated in the title. In analogy with quantum mechanics, at the core of the approach are two notions: states and (generalized) observables. This motivates us to distinguish between mathematical and physical dynamical systems. The first class deals with mathematical models and states (solutions) only. The second one adds physical realizations and observables, i.e. all methods of extracting useful information. Observables include: renormalization, optimal gauging, covering–coloring, discretization, tensorial measures of chaos, etc. The corresponding algorithms are correlated to Kolmogorov complexity and are intrinsic parts of observables, and thus of physical systems. The approach is illustrated by examples.