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ACCURATE HIGH ORDER COMPUTATION OF INVARIANT MANIFOLDS FOR LONG PERIODIC ORBITS OF MAPS AND EQUILIBRIUM STATES OF PDE

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Date Issued:
2020
Abstract/Description:
The study of the long time behavior of nonlinear systems is not effortless, but it is very rewarding. The computation of invariant objects, in particular manifolds provide the scientist with the ability to make predictions at the frontiers of science. However, due to the presence of strong nonlinearities in many important applications, understanding the propagation of errors becomes necessary in order to quantify the reliability of these predictions, and to build sound foundations for future discoveries. This dissertation develops methods for the accurate computation of high-order polynomial approximations of stable/unstable manifolds attached to long periodic orbits in discrete time dynamical systems. For this purpose a multiple shooting scheme is applied to invariance equations for the manifolds obtained using the Parameterization Method developed by Xavier Cabre, Ernest Fontich and Rafael De La Llave in [CFdlL03a, CFdlL03b, CFdlL05].
Title: ACCURATE HIGH ORDER COMPUTATION OF INVARIANT MANIFOLDS FOR LONG PERIODIC ORBITS OF MAPS AND EQUILIBRIUM STATES OF PDE.
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Name(s): Gonzalez, Jorge L., author
Mireles-James, Jason , Thesis advisor
Florida Atlantic University, Degree grantor
Department of Mathematical Sciences
Charles E. Schmidt College of Science
Type of Resource: text
Genre: Electronic Thesis Or Dissertation
Date Created: 2020
Date Issued: 2020
Publisher: Florida Atlantic University
Place of Publication: Boca Raton, Fla.
Physical Form: application/pdf
Extent: 155 p.
Language(s): English
Abstract/Description: The study of the long time behavior of nonlinear systems is not effortless, but it is very rewarding. The computation of invariant objects, in particular manifolds provide the scientist with the ability to make predictions at the frontiers of science. However, due to the presence of strong nonlinearities in many important applications, understanding the propagation of errors becomes necessary in order to quantify the reliability of these predictions, and to build sound foundations for future discoveries. This dissertation develops methods for the accurate computation of high-order polynomial approximations of stable/unstable manifolds attached to long periodic orbits in discrete time dynamical systems. For this purpose a multiple shooting scheme is applied to invariance equations for the manifolds obtained using the Parameterization Method developed by Xavier Cabre, Ernest Fontich and Rafael De La Llave in [CFdlL03a, CFdlL03b, CFdlL05].
Identifier: FA00013468 (IID)
Degree granted: Dissertation (Ph.D.)--Florida Atlantic University, 2020.
Collection: FAU Electronic Theses and Dissertations Collection
Note(s): Includes bibliography.
Subject(s): Invariant manifolds
Nonlinear systems
Diffeomorphisms
Parabolic partial differential equations
Differential equations, Partial
Held by: Florida Atlantic University Libraries
Sublocation: Digital Library
Persistent Link to This Record: http://purl.flvc.org/fau/fd/FA00013468
Use and Reproduction: Copyright © is held by the author with permission granted to Florida Atlantic University to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Use and Reproduction: http://rightsstatements.org/vocab/InC/1.0/
Host Institution: FAU
Is Part of Series: Florida Atlantic University Digital Library Collections.