SYSTEMS OF ODE, Mathematics

Assignment Help:
Problem 1 Let ~x0 = A~x and y
0 = B~y be two 2  2 linear systems of ODE.
(1) Suppose that A and B have the same purely imaginary eigenvalues. Prove that these systems
are topologically conjugate.
(2) Suppose that A and B have di erent purely imaginary eigenvalues. Prove that the ODE
systems are not topologically conjugate.
(3) Suppose A has eigenvalues 0,  and B has eigenvalues 0, . Prove theta the ODE systems are
topologically conjugate if and only if and  have the same sign.
(4) Prove that if A has purely imaginary eigenvalues, and B has real eigenvalues, then the ODE
systems are not topologically conjugate.
(5) Use the information above as well as the theorems from class to provide complete classi cation
of dynamics two-dimensional linear systems of ODE by conjugacy

Related Discussions:- SYSTEMS OF ODE

Variance, Variance Consider the example of investment opportunities. Th...

Variance Consider the example of investment opportunities. The expected gains were Rs.114 and Rs.81 respectively. The fact is that an investor also looks at the dispersion befo

Dividing whole numbers, Dividing Whole Numbers: Example: Divide 3...

Dividing Whole Numbers: Example: Divide 347 by 5. Solution:                      Beginning from the left of the dividend, the divisor is divided into the

Chi square distribution, Chi Square Distribution Chi square was first ...

Chi Square Distribution Chi square was first utilized by Karl Pearson in 1900. It is denoted by the Greek letter χ 2 . This contains only one parameter, called the number of d

Largest number of vertices in a graph, a) Specify that a tree has at least ...

a) Specify that a tree has at least 2 vertices of degree 1.                               b) What is the largest number of vertices in a graph with 35 edges if all vertices are

Metric Units, How do I convert metric units?

How do I convert metric units?

Solve 6 sin ( x/2)= 1 on [-20, Solve 6 sin ( x/2)= 1 on [-20,30] Soluti...

Solve 6 sin ( x/2)= 1 on [-20,30] Solution Let's first work out calculator of the way since that isn't where the difference comes into play. sin( x/2)= 1/6   ⇒x/2= sin

Graph and algebraic methods , To answer each question, use the function t(r...

To answer each question, use the function t(r) = d , where t is the time in hours, d is the distance in miles, and r is the rate in miles per hour. a. Sydney drives 10 mi at a c

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd