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Virginia Tech

A Newton Method For The Continuation Of Invariant Tori

Abstract

dc:description.abstract

This thesis proposes a novel method for locating a p-dimensional invariant torus of an n-dimensional map. A set of non-linear equations is formulated and solved using the Newton-Raphson scheme. The method requires a set of sampled points on a guess invariant torus. An interpolant is passed through these points to compute the pointwise shift on the invariant torus, which is used to formulate the equation of invariance for the torus under the given map. The principal application of this method is to locate invariant tori of continuous systems. These tori occur for continuous dynamical systems having quasiperiodic orbits in state space. The discretization of the continuous system in terms of a map is accomplished in terms of its flow function. Results for one-dimensional invariant tori in two and three-dimensional state space and for two-dimensional invariant tori in three and four-dimensional maps are presented.

Degree

thesis:*
Name thesis:degree_name
Master of Science
Level thesis:degree_level
masters
Discipline thesis:degree_discipline
Engineering Science and Mechanics
Department dc:contributor.department
Engineering Science and Mechanics
Grantor dc:publisher
Virginia Tech
Year dc:date.issued
2004

Author and committee

dc:creator, dc:contributor.*
Author dc:creator
  • Thakur, Gunjan Singh
Chair dc:contributor.committeechair
  • Dankowicz, Harry J.
Committee members dc:contributor.committeemember
  • Kachroo, Pushkin
  • Hendricks, Scott L.

Subjects

dc:subject × 5

Rights

dc:rights
Statement dc:rights
  • In Copyright

Identifiers

dc:identifier.*
Dc Identifier Other
etd-07282004-141952
OAI identifier oai:identifier
oai:vtechworks.lib.vt.edu:10919/43918

Chain of custody

source
Harvested from
Virginia Tech
Base URL
vtechworks.lib.vt.edu/oai/request
Last updated
2026-07-22
Source record
OAI-PMH GetRecord
citation

Thakur, Gunjan Singh. A Newton Method For The Continuation Of Invariant Tori. masters thesis, Virginia Tech, 2004. http://hdl.handle.net/10919/43918