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  is given by the Fundamental Solution Theorem
The initial value problem for the non-autonomous linear system 
Chapter 2 part B , ,  can arise from linearization about a periodic orbit. In this case
is the periodic orbit and
is another trajectory close to the orbit. sketch Higher order terms
are dropped to arrive at , but the solution of  may give a good approximation to the
behavior of the nearby trajectory. See chapter 4 . Floquet theory discusses the solution of 
when is periodic. Let the period be . The fundamental matrix solution corresponding to  is the solution of the initial value problem
.  is the solution at time of the initial value problem that begins at time
solves  then
solves . Note th...
View Full Document
This document was uploaded on 02/24/2014 for the course MATH 512 at Washington State University .
- Fall '14