Infinite-Dimensional Dynamical Systems and Projections
| dc.contributor.advisor | Yorke, James A | en_US |
| dc.contributor.author | Ott, William Raymond | en_US |
| dc.contributor.department | Mathematics | en_US |
| dc.date.accessioned | 2004-05-31T20:21:35Z | |
| dc.date.available | 2004-05-31T20:21:35Z | |
| dc.date.issued | 2004-04-27 | en_US |
| dc.description.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. | en_US |
| dc.format.extent | 493179 bytes | |
| dc.format.mimetype | application/pdf | |
| dc.identifier.uri | http://hdl.handle.net/1903/248 | |
| dc.language.iso | en_US | |
| dc.relation.isAvailableAt | Digital Repository at the University of Maryland | en_US |
| dc.relation.isAvailableAt | University of Maryland (College Park, Md.) | en_US |
| dc.subject.pqcontrolled | Mathematics | en_US |
| dc.title | Infinite-Dimensional Dynamical Systems and Projections | en_US |
| dc.type | Dissertation | en_US |
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