Geometry of Chaos: Advanced computational approach to treating chaotic dynamics of environmental radioactivity systems I General Formalism

In the paper we go on a development of eective new chaos geomentry and non-linear analysis technique to studying chaotic features of dierent nature systems. Here there are presented a general for,alism of a chaos-geometrical appraoch to treating, analysing, modelling and forecasting chaotic dynamics of environmental radioactivity systems. A usually, an approach combines together application of the advanced mltifractal formalism, advanced mutual information scheme, Grrasberger-Procachi algorythm, Lyapunov exponent's analysis, method of precicted phase trajectories, memory functions method , neural networks algorythms etc