A topological time-delay embedding theorem for infinite-dimensional cocycle dynamical systems

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May 2008, 9(3&4, May): 731-741. doi: 10.3934/dcdsb.2008.9.731

A topological time-delay embedding theorem for infinite-dimensional cocycle dynamical systems

1.	Mathematical Institute, University of Warwick, Coventry CV4 7AL, United Kingdom

Received March 2007 Revised August 2007 Published February 2008

Abstract
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This paper gives a version of the Takens time delay embedding theorem that is valid for non-autonomous and stochastic infinite-dimensional dynamical systems that have a finite-dimensional attractor. A key ingredient is a result showing that a single linear map from the phase space into a sufficiently high dimensional Euclidean space is one-to-one between most realizations of the attractor and its image.

Keywords: the Takens time-delay embedding theorem., non-autonomous attractor, random attractor, thickness exponent.

Mathematics Subject Classification: Primary: 37B55, 37L30, 35B4.

Citation: J. C. Robinson. A topological time-delay embedding theorem for infinite-dimensional cocycle dynamical systems. Discrete & Continuous Dynamical Systems - B, 2008, 9 (3&4, May) : 731-741. doi: 10.3934/dcdsb.2008.9.731

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