Distinguishing smooth functions by a finite number of point values, and a version of the Takens embedding theorem
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. ISSN 0167-2789Full text not available from this repository.
Official URL: http://dx.doi.org/10.1016/jk.physd.2004.04.004
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|
|Subjects:||Q Science > QA Mathematics
Q Science > QC Physics
|Journal or Publication Title:||PHYSICA D-NONLINEAR PHENOMENA|
|Publisher:||ELSEVIER SCIENCE BV|
|Date:||1 September 2004|
|Number of Pages:||22|
|Page Range:||pp. 45-66|
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