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    Infinite-Dimensional Dynamical Systems and Projections

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    No. of downloads: 1035

    Date
    2004-04-27
    Author
    Ott, William Raymond
    Advisor
    Yorke, James A
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    Abstract
    We address three problems arising in the theory of infinite-dimensional dynamical systems. First, we study the extent to which the Hausdorff dimension and the dimension spectrum of a fractal measure supported on a compact subset of a Banach space are affected by a typical mapping into a finite-dimensional Euclidean space. We prove that a typical mapping preserves these quantities up to a factor involving the thickness of the support of the measure. Second, we prove a weighted Sobolev-Lieb-Thirring inequality and we use this inequality to derive a physically relevant upper bound on the dimension of the global attractor associated with the viscous lake equations. Finally, we show that in a general setting one may deduce the accuracy of the projection of a dynamical system solely from observation of the projected system.
    URI
    http://hdl.handle.net/1903/248
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