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

Find out the mean wait in line - probability, Example of Probability I...

Example of Probability Illustration:  It has been determined that the probability density function for the wait in line at a counter is specified by, In which t is the

Sketch the graph f ( x ) = - x5 + (5/2 )x4 + (40/3) x3 + 5, Sketch the grap...

Sketch the graph of the below function. f ( x ) = - x 5 + (5/2 )x 4 + (40/3) x 3 + 5 Solution : Whenever we sketch a graph it's good to have a few points on the graph to

Polya’s first and second principle:-mathematical problem, Mathematical Prob...

Mathematical Problem Solving In 1945, mathematician George Polya (1887-1985) published a book titled How To Solve It in which he demonstrated his approach to solving problems.

What is the marginal product of labor function, Your engineering department...

Your engineering department estimated the following production function. Q = 15L 2 - 0.5L 3 a. What is the marginal product of labor function, MP L ? b. What is the aver

Tied rankings, Tied Rankings A slight adjustment to the formula is mad...

Tied Rankings A slight adjustment to the formula is made if several students tie and have the similar ranking the adjustment is: (t 3 - t)/12 Whereas t = number of tied

Statistics, If a mean score is 89 with a standard deviation of 8 points. Wh...

If a mean score is 89 with a standard deviation of 8 points. What is the least score you can make and be in the top 20%?

Variation, If p=10 when q=2,find p when q=5

If p=10 when q=2,find p when q=5

Arithmetic progression, the radii of circular base of right circular cylind...

the radii of circular base of right circular cylinder and cone are in the ratio of 3:4 and their height are in the ratio of the 2:3 what is the ratio of their volume?

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