Information-Based Partitioning of the Dynamical System’s Domain

Abstract We suggest a method of discretization of the domain of dynamical systems based on observations. The method utilizes $$\varepsilon $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ε</mml:mi> </mml:math> -entropy, $$\varepsilon $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ε</mml:mi> </mml:math> -capacity, and the introduced $$\varepsilon $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ε</mml:mi> </mml:math> -information. It results in the partition of the system’s domain to the cells of equal diameters that allows representation of the system in the terms of discrete dynamics and its numerical analysis and modelling.