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Distinguishing smooth functions by a finite number of point values, and a version of the Takens embedding theorem
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UNSPECIFIED (2004) Distinguishing smooth functions by a finite number of point values, and a version of the Takens embedding theorem. PHYSICA D-NONLINEAR PHENOMENA, 196 (1-2). pp. 45-66. doi:10.1016/jk.physd.2004.04.004 ISSN 0167-2789.
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Official URL: http://dx.doi.org/10.1016/jk.physd.2004.04.004
Abstract
We prove a general result showing that a finite-dimensional collection of smooth functions whose differences cannot vanish to infinite order can be distinguished by their values at a finite collection of points; this theorem is then applied to the global attractors of various dissipative parabolic partial differential equations. In particular for the one-dimensional complex Ginzburg-Landau equation and for the Kuramoto-Sivashinsky equation, we show that a finite number of measurements at a very small number of points (two and four, respectively) serve to distinguish between different elements of the attractor: this gives an infinite-dimensional version of the Takens time-delay embedding theorem. (C) 2004 Elsevier B.V. All rights reserved.
| Item Type: | Journal Article | ||||
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| Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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| Journal or Publication Title: | PHYSICA D-NONLINEAR PHENOMENA | ||||
| Publisher: | ELSEVIER SCIENCE BV | ||||
| ISSN: | 0167-2789 | ||||
| Official Date: | 1 September 2004 | ||||
| Dates: |
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| Volume: | 196 | ||||
| Number: | 1-2 | ||||
| Number of Pages: | 22 | ||||
| Page Range: | pp. 45-66 | ||||
| DOI: | 10.1016/jk.physd.2004.04.004 | ||||
| Publication Status: | Published |
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