This preview shows page 1. Sign up to view the full content.
Unformatted text preview: value problem for an autonomous linear system
, , can arise from linearization about an equilibrium point. As we shall see in chapter 5, when
hyperbolic this system gives a good approximation to the behavior of nearby trajectories.
sketch The solution of [1] is given by the Fundamental Solution Theorem
.
The initial value problem for the nonautonomous linear system [1]
is 13
Chapter 2 part B , , [2] can arise from linearization about a periodic orbit. In this case
, where
is the periodic orbit and
is another trajectory close to the orbit. sketch Higher order terms
are dropped to arrive at [2], but the solution of [2] may give a good approximation to the
behavior of the nearby trajectory. See chapter 4 . Floquet theory discusses the solution of [2]
when is periodic. Let the period be . The fundamental matrix solution corresponding to [2] is the solution of the initial value problem
. [3] is the solution at time of the initial value problem that begins at time
solves [3] then
solves [2]. Note th...
View
Full
Document
This document was uploaded on 02/24/2014 for the course MATH 512 at Washington State University .
 Fall '14
 MarcEvans

Click to edit the document details