Title page for ETD etd-07282004-141952


Type of Document Master's Thesis
Author Thakur, Gunjan Singh
URN etd-07282004-141952
Title A Newton Method For The Continuation Of Invariant Tori
Degree Master of Science
Department Engineering Science and Mechanics
Advisory Committee
Advisor Name Title
Dankowicz, Harry J. Committee Chair
Hendricks, Scott L. Committee Member
Kachroo, Pushkin Committee Member
Keywords
  • Dynamical system
  • Continuation
  • Nonlinear system
  • Invarinat tori
  • Newton method
Date of Defense 2004-07-20
Availability restricted
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.

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