Generating functions in Symplectic Geometry

• Autores: Aguirre Enciso, Josué Alonso, Gálvez Pérez, Rodolfo José
• Formato: artículo
• Fecha de Publicación: 2019
• Institución: Universidad Nacional Mayor de San Marcos
• Repositorio: Revistas - Universidad Nacional Mayor de San Marcos
• Lenguaje: español
• OAI Identifier: oai:ojs.csi.unmsm:article/15721
• Enlace del recurso: https://revistasinvestigacion.unmsm.edu.pe/index.php/matema/article/view/15721
• Nivel de acceso: acceso abierto
• Materia: Symplectic Manifold; Generating functions; vector field.; Variedad Simpléctica; Funciones Generadoras; Campos vectoriales; Simpléctomorfismo

In this work, we present a brief introduction to Symplectic Geometry relating its origin with the Physics. Then we present the formal definition of symplectic manifold and some important results, with this we consider a function AH;N defined in the Cartesian product of the symplectic manifold (ℝ2n; ω0). Here we make an analysis with the fact that the critical points of this function are related in a biunivocal way to the fixed points of the flow Φt of the symplectic manifold (ℝ2n; ω0)in time t = 1 this thanks to the Hamiltonian diferential equations via the generating functions.