Global Attractors: Topology and Finite-Dimensional Dynamics
نویسنده
چکیده
Many a dissipative evolution equation possesses a global attractor A with finite Hausdorff dimension d. In this paper it is shown there is an embedding X of A into IR , with N = [2d+2], such that X is the global attractor of some finite-dimensional system on IR with trivial dynamics on X. This allows the construction of a discrete dynamical system on IR which reproduces the dynamics of the time T map on A, and has an attractor within an arbitrarily small neighbourhood of X. If the Hausdorff dimension is replaced by the fractal dimension, a similar construction can be shown to hold good even if one restricts to orthogonal projections rather than arbitrary embeddings.
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