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Retracts, fixed point index and differential equations

Retractos, índice de punto fijo y ecuaciones diferenciales

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Abstract

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.

Resumen

Algunos problemas de las ecuaciones diferenciales evolucionan hacia la Topología desde un origen analítico. 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 teoría de retractos y el índice de punto fijo se han convertido en herramientas muy útiles para el estudio de estas cuestiones.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada Facultad de Ciencias, Universidad de Granada, 18071, Granada, Spain

    Rafael Ortega

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  1. Rafael Ortega
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Correspondence to Rafael Ortega.

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Dedicated to E. Norman Dancer

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Ortega, R. Retracts, fixed point index and differential equations. Rev. R. Acad. Cien. Serie A. Mat. 102, 89–100 (2008). https://doi.org/10.1007/BF03191813

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  • DOI: https://doi.org/10.1007/BF03191813

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