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The New Jersey Institute of Technology's
Electronic Theses & Dissertations Project

Title: High-order adaptive methods for computing invariant manifolds of maps
Author: Wrobel, Jacek K.
View Online: njit-etd2011-063
(xvi, 134 pages ~ 5.2 MB pdf)
Department: Department of Mathematical Sciences
Degree: Doctor of Philosophy
Program: Mathematical Sciences
Document Type: Dissertation
Advisory Committee: Goodman, Roy (Committee chair)
Blackmore, Denis L. (Committee member)
Bose, Amitabha Koshal (Committee member)
Moore, Richard O. (Committee member)
Mosher, Lee D. (Committee member)
Date: 2011-05
Keywords: Inconvenient manifold
Computer-aided geometric design
Numerical algorithm
Availability: Unrestricted

The author presents efficient and accurate numerical methods for computing invariant manifolds of maps which arise in the study of dynamical systems. In order to decrease the number of points needed to compute a given curve/surface, he proposes using higher-order interpolation/approximation techniques from geometric modeling. He uses B´ezier curves/triangles, fundamental objects in curve/surface design, to create adaptive methods. The methods are based on tolerance conditions derived from properties of B´ezier curves/triangles. The author develops and tests the methods for an ordinary parametric curve; then he adapts these methods to invariant manifolds of planar maps. Next, he develops and tests the method for parametric surfaces and then he adapts this method to invariant manifolds of three-dimensional maps.

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