Poincaré’s method of normal forms in the study of factors of Production

Abstract

As the main factors of production, the paper considers physical capital and labor resources. The study of the behavior of the main factors of production is based on the analysis of the volume of investment in them, the depreciation of physical capital and changes in the volume of labor resources. Most of the studies on this topic do not address issues related to distortions in financing and their possible consequences for the main factors of production. To assess these consequences, formulas were derived that include partial derivatives of investment volumes for each of the main factors. The use of these formulas helps to develop an investment algorithm that contributes to the sustainable growth of the main factors of production. The method of Poincaré normal forms was chosen as the main research method, which allows us to simplify the initial problem and reduce it to an analysis in a linear form. A classification of possible variants of eigenvalues, the resulting linear form was carried out. The behavior of the main factors of production depending on the found eigenvalues is determined. This method allows you to get more understandable results and draw more accurate conclusions. The results obtained were tested in a number of federal districts of Russia and a number of EU countries. Testing showed a qualitative match with the real state of the main factors of production. This suggests that the developed investment algorithm can be applied in practical conditions and contribute to the achievement of stable growth in various regions of Russia. This study is important for understanding and optimizing production processes and economic development. It provides a basis for developing effective investment and decision-making strategies that promote both a balanced and directed development of the main factors of production.