Retracts, fixed point index and differential equations
نویسندگان
چکیده
Some problems in differential equations evolve towards Topology from an analytical origin. Two such problems will be discussed: the existence of solutions asymptotic to the equilibrium and the stability of closed orbits of Hamiltonian systems. The theory of retracts and the fixed point index have become useful tools in the study of these questions. Retractos, ı́ndice de punto fijo y ecuaciones diferenciales Resumen. Algunos problemas de las ecuaciones diferenciales evolucionan hacia la Topologı́a desde un origen analı́tico. Se discutirán dos problemas de este tipo: la existencia de soluciones asintóticas al equilibrio y la estabilidad de las órbitas cerradas de los sistemas Hamiltonianos. La teorı́a de retractos y el ı́ndice de punto fijo se han convertido en herramientas muy útiles para el estudio de estas cuestiones.
منابع مشابه
Retracts , fixed point index and differential equations ∗ Rafael Ortega
Many problems in the theory of differential equations were initially treated with analytic techniques and later evolved towards more topological approaches. Perhaps the most paradigmatic case is found in the study of nonlinear boundary value problems. The classical proofs based on successive approximations or in the implicit function theorem were soon replaced by the use of fixed points and deg...
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تاریخ انتشار 2008