| Summary: | <p>Work is devoted to the development of the theoretical foundations of the universal new relativistic chaos-geometric and quantum-dynamic approach that consistently includes a number of new relativistic quantum models and a number of new or improved methods of analysis (correlation integral, fractal analysis, algorithms, average mutual information, false nearest neighbors, Lyapunov exponents, surrogate data, non-linear prediction, spectral methods, etc.) to solve problems of complete modelling relativistic chaotic dynamics in an electromagnetic field. For a number of atomic systems there are firstly discovered availability of a relativistic quantum chaos and obtained the corresponding quantitative data on the chaos characteristics.</p>
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