THE APPLICATION OF INVARIANTS IN STUDYING SPECIAL POINTS OF CERTAIN CLASSES OF DIFFERENTIAL EQUATIONS

Аннотация

This paper explores the role of invariants in the analysis of special points within various classes of differential equations. By leveraging invariants, the study provides a framework for simplifying the identification and characterization of equilibrium points, singularities, and other critical features. The results demonstrate that invariants offer powerful tools for analyzing the structure and solutions of differential equations, especially in complex systems. KEYWORDS Differential Equations, Invariants, Special Points, Equilibrium Points, Singularities, Bifurcations, Non-linear Systems, Symmetry Analysis, Conserved Quantities, Partial Differential Equations (PDEs).