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Dynamical systems and shapes

Sistemas dinámicos y formas

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Abstract

This survey is an introduction to some of the methods, techniques and concepts from algebraic topology and related areas (homotopy theory, shape theory) which can be fruitfully applied to study problems concerning continuous dynamical systems. To this end two instances which exemplify the interaction between topology and dynamics are considered, namely, Conley’s index theory and the study of some properties of certain attractors.

Resumen

Este artículo panorámico constituye una introducción a algunos de los métodos, técnicas y conceptos que, desde la topología algebraica y otras áreas afines (teoría de homotopía, teoría de la forma), permiten abordar problemas que se plantean en el marco de los sistemas dinámicos continuos. Para ello se presentan dos situaciones que ejemplifican esta interacción entre topología y dinámica, como son la construcción del índice de Conley y el estudio de algunas propiedades de ciertos atractores.

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  1. Facultad de Matemáticas, Departamento de Geometría y Topología, Universidad Complutense de Madrid, 28084, Madrid, Spain

    J. J. Sánchez-Gabites

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Sánchez-Gabites, J.J. Dynamical systems and shapes. Rev. R. Acad. Cien. Serie A. Mat. 102, 127–159 (2008). https://doi.org/10.1007/BF03191815

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