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

Mathematics- in our lives , MATHEMATICS - IN OUR LIVES : What is the mo...

MATHEMATICS - IN OUR LIVES : What is the most obvious example of mathematics in your life? To many of us it is the maths that we studied in school. But is that all the mathemat

Trigonometry, If sec A = x+i/x, prove that sec A + tan A = 2x or 1/2x

If sec A = x+i/x, prove that sec A + tan A = 2x or 1/2x

Compute the derivative, Write an octave program that will take a set of poi...

Write an octave program that will take a set of points {x k , f k } representing a function and compute the derivative at the same points x k using 1. 2-point forward di erence

HELP, WHAT TWO SIX DIDGIT NUMBERS CAN YOU ADD 984,357

WHAT TWO SIX DIDGIT NUMBERS CAN YOU ADD 984,357

How much greater is 0.0543 than 0.002, How much greater is 0.0543 than 0.00...

How much greater is 0.0543 than 0.002? To ?nd out how much greater a number is, you required to subtract; 0.0543 - 0.002 = 0.0523. For subtract decimals and line the numbers up

Triangulos rectangulos y no rectangulos, el extremo de un poste que partió ...

el extremo de un poste que partió 8.45 metros de la base del poste y forma con el suelo un angulo de 40 grados 28 minutos.hallar la altura original del poste

Fractions, you need to cut the proper to cut 2''*4*8 long studs to the prop...

you need to cut the proper to cut 2''*4*8 long studs to the proper length to make a finished wall 8" in height underneath the studs there will be a double plate made up of two piec

Rounding, the number is 605176 the underline digit is 0

the number is 605176 the underline digit is 0

Volume of grains in the silo , The volume of grains in a silo at a particul...

The volume of grains in a silo at a particular time (measured in hours) is given by V (t) = 4t(3-t) m3. Find the rate of change of the volume of grains in the silo from first princ

Math help until tuesday, I need help with pre algebra in 5th grade intermid...

I need help with pre algebra in 5th grade intermidate school math until Tuesday afternoon please

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