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

Percentage, By selling a violin for $4950, giving a 10% discount on the mar...

By selling a violin for $4950, giving a 10% discount on the marked price, a trader gained $950 on his investment, Find, Cost price.

Newtons method , Newton's Method : If x n is an approximation a solution ...

Newton's Method : If x n is an approximation a solution of f ( x ) = 0 and if given by, f ′ ( x n ) ≠ 0 the next approximation is given by

How many people should she expect not to show, Laura is planning her weddin...

Laura is planning her wedding. She expects 230 people to attend the wedding, but she has been told that around 5% typically don't show. About how many people should she expect not

Differentiation, how to write assignment of the application of differentiat...

how to write assignment of the application of differentiation in science

Real analysis, .find lim sup Ek and liminf Ek of Ek=[(-(1/k),1] for k odd a...

.find lim sup Ek and liminf Ek of Ek=[(-(1/k),1] for k odd and liminf Ek=[(-1,(1/k)] for k even

How will you use the Gantt chart for solving the sequencing, How will you u...

How will you use the Gantt chart for solving the sequencing problem?

What is the diameter of the pipe along with the insulation, A pipe has a di...

A pipe has a diameter of 2.5 inches. Insulation which is 0.5 inches thick is placed around the pipe. What is the diameter of the pipe along with the insulation around it? The i

Trigonometry, Show that the radius of the circle,passing through the centre...

Show that the radius of the circle,passing through the centre of the inscribed circle of a triangle and any two of the centres of the escribed circles,is equal to the diameter of t

Determine the eigenvalues and eigenvectors of the matrix, Determine the eig...

Determine the eigenvalues and eigenvectors of the subsequent matrix. Solution : The first thing that we require to do is determine the eigen-values. It means we require

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