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

Permuation and combination, how many words can be formed from letters of wo...

how many words can be formed from letters of word daughter such that each word contain 2vowles and 3consonant

Determine the probability of tossing a head, Q. Determine the probability o...

Q. Determine the probability of tossing a head? Let B represent the event of tossing a heads with the nickel in example 2. Find P(B). Solution:   S = {(H, H), (H, T), (T, H

Graph y = cos ( x ) - common graph, Graph y = cos (x) Solution: There ...

Graph y = cos (x) Solution: There actually isn't a whole lot to this one.  Given the graph for -4 ? ≤ x ≤ 4 ? . Note that we can put all values of x in cosine (that wo

Precalculus help, tsunami equation A sin (b * t) + k what is b supposed t...

tsunami equation A sin (b * t) + k what is b supposed to be if t is time a is amplitude and k is average water level (not exact value of b just what is it)

Determine the transfer function, A digital filter has zero at z=a and poles...

A digital filter has zero at z=a and poles at z=b andz=c, where a, b, c are the real constants. Determine the transfer function and the frequency response function of the filter an

Applied Math, Calucations of gradients find f Graph some level curve f=cons...

Calucations of gradients find f Graph some level curve f=const. f=9x^2 = 4y^2

Class 10, chapter permutation & combination ex :4.6

chapter permutation & combination ex :4.6

Introduction to computers, What is a Computer? A computer is ...

What is a Computer? A computer is an electronic device which senses or accepts input data, performs operations or computations on the data in a pre-arranged sequence

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