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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

J. C. Robinson 1,

1. 

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

Received  March 2007 Revised  August 2007 Published  February 2008

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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