Physical and mathematical foundations of measurements in nonlinear dynamic systems

Abstract

Physical and mathematical bases of measurements in physical non-linear dynamical systems are formulated. Physical properties, common to different systems, include: interval physical values; different modes of dynamics (including chaotic); strong dependence on the initial conditions; exposure to noise. We have used mathematical tools and methods of the dynamic chaos theory, open systems theory, fractal analysis: intervals of quantities values, fractal dimension, predictability time, model equation and others. New results and models are important for creating lasers with high stabilization of characteristics and practical application of solitons.