Existencia de Soluciones Periódicas de una Ecuación Hamiltoneana Basado en el Grado Topológico
DOI:
https://doi.org/10.17268/sel.mat.2014.02.06Keywords:
Hamiltoneano, simplectomorsmos, variedades simplecticas, grado topologicoAbstract
En este trabajo probamos un resultado de existencia para soluciones periodicas de una ecuacion Hamiltoneana partcular dependiente del tiempo, la cual es asumida a ser asintoticamente lineal. Las soluciones periodicas son encontradas como puntos crticos de un problema variacional abstracto en un espacio de Hilbert real. Por medio de una reduccion a un punto de silla este problema es reducido al problema de encontrar puntos crticos de una funcion denida sobre un subespacio de dimension nita. Los puntos crticos son entonces encontrados usando argumentos del grado topologico.
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