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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations
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Dimensions, Embeddings, and Attractors (Hardcover)
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Dimensions, Embeddings, and Attractors (Hardcover)
Series: Cambridge Tracts in Mathematics
Expected to ship within 12 - 17 working days
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This accessible research monograph investigates how
'finite-dimensional' sets can be embedded into finite-dimensional
Euclidean spaces. The first part brings together a number of
abstract embedding results, and provides a unified treatment of
four definitions of dimension that arise in disparate fields:
Lebesgue covering dimension (from classical 'dimension theory'),
Hausdorff dimension (from geometric measure theory), upper
box-counting dimension (from dynamical systems), and Assouad
dimension (from the theory of metric spaces). These abstract
embedding results are applied in the second part of the book to the
finite-dimensional global attractors that arise in certain
infinite-dimensional dynamical systems, deducing practical
consequences from the existence of such attractors: a version of
the Takens time-delay embedding theorem valid in spatially extended
systems, and a result on parametrisation by point values. This book
will appeal to all researchers with an interest in dimension
theory, particularly those working in dynamical systems.
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