Sistemas Dinámicos sobre la Esfera

Abstract

The dynamic systems on the sphere allow to model diverse phenomena in areas such as physics, chemistry, biology, etc. However, in most cases it is not possible to find a general solution for these systems. Therefore, in this work we present a useful mechanism for obtaining qualitative solutions of dynamic systems both in the plane and in the sphere, without the need to solve them explicitly, such a tool is the well-known Poincaré-Bendixson theorem. Later, examples are given of some dynamic systems in the plane as in the sphere and some applications, where the importance of the aforementioned theorem is shown. Finally concluding that said theorem, rather than an important result, turns out to be indispensable in the study of said systems.