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The pullback attractor

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Attractors for infinite-dimensional non-autonomous dynamical systems

Part of the book series: Applied Mathematical Sciences ((AMS,volume 182))

Abstract

The global attractor, whose well established definition we recall below, is an object that captures the asymptotic behaviour of autonomous systems. The aim of this chapter is to introduce the ‘pullback attractor’, which seems to be the correct generalisation of this concept for use with non-autonomous processes. We pay particular attention to how this non-autonomous definition relates to the autonomous one.

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Notes

  1. 1.

    The global attractor is the minimal compact set that attracts every bounded subset of the phase space, see Definition 1.5 and Lemma 1.6. While this definition is indeed ‘well established’, there are many possible definitions of ‘an attractor’, and it is probably not the case that there is one canonical definition (see Milnor 1985, for example).

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Author information

Authors and Affiliations

  1. Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, São Carlos, SP, Brazil

    Alexandre N. Carvalho

  2. Departamento de Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, C/ Tarfia s/n, Seville, Spain

    José A. Langa

  3. Mathematics Institute, University of Warwick, Coventry, UK

    James C. Robinson

Authors
  1. Alexandre N. Carvalho
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  2. José A. Langa
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  3. James C. Robinson
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Carvalho, A.N., Langa, J.A., Robinson, J.C. (2013). The pullback attractor. In: Attractors for infinite-dimensional non-autonomous dynamical systems. Applied Mathematical Sciences, vol 182. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4581-4_1

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