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

GEOMETRY, DIFFERENCE BETWEEN RIGHT ANGLE AND SCALENE

DIFFERENCE BETWEEN RIGHT ANGLE AND SCALENE

Linear programming problem., Ask question #Minimum 100 words acca paper mil...

Ask question #Minimum 100 words acca paper mill produces two grades of paper viz.,xand y.Bacause of raw material restrictions, it cannot produce more than 400 tones of grade x pape

Example of subtraction of fractions, Example of Subtraction of Fractions: ...

Example of Subtraction of Fractions: 1/3 + 1/6 + 1/8 = ____ Using trial & error we could search that 24 is the LCD or smallest number in which 3, 6, and 8 will all divide w

Forecast errors, Forecast Errors Differences among actual results and ...

Forecast Errors Differences among actual results and predictions may arise from many reasons. They may arise from random influences, usual sampling errors, option of the wrong

Find their present ages of son and father, When the son will be as old as t...

When the son will be as old as the father today their ages will add up to 126 years. When the father was old as the son is today, their ages add upto 38 years.  Find their present

Second order differential equations, In the earlier section we looked at fi...

In the earlier section we looked at first order differential equations. In this section we will move on to second order differential equations. Just as we did in the previous secti

Probability, An unbiased die is tossed twice .Find the probability of getti...

An unbiased die is tossed twice .Find the probability of getting a 4,5,6 on the first toss and a 1,2,3,4 on the second toss

The blood pressure over two heart beats, At rest, the human heart beats onc...

At rest, the human heart beats once every second. At the strongest part of the beat, a person's blood pressure peaks at 120mmHg. At the most relaxed part of the beat, a person's bl

Calculas, how to deal with integration by parts

how to deal with integration by parts

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