Generating functions in Symplectic Geometry
DOI:
https://doi.org/10.15381/pes.v21i2.15721Keywords:
Symplectic Manifold, Generating functions, vector field.Abstract
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.
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Copyright (c) 2019 Josué Alonso Aguirre Enciso, Rodolfo José Gálvez Pérez
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