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

Number system, NATURAL NUMBERS The numbers 1, 2, 3, 4.... Are called as...

NATURAL NUMBERS The numbers 1, 2, 3, 4.... Are called as natural numbers, their set is shown by N. Hence N = {1, 2, 3, 4, 5....} WHOLE NUMBERS The numbers 0, 1, 2, 3, 4

Slope-intercept form, Slope-intercept form The ultimate special form of...

Slope-intercept form The ultimate special form of the equation of the line is possibly the one that most people are familiar with.  It is the slope-intercept form.  In this if

Find the interval of validity, Solve the subsequent IVP and find the interv...

Solve the subsequent IVP and find the interval of validity for the solution. y' + (4/x) y = x 3 y 2 ,       y(2) = - 1,  x > 0 Solution Thus, the first thing that we re

Determine the nand gate, Find out the two inputs when the NAND gate output ...

Find out the two inputs when the NAND gate output will be low. Ans. The output of NAND gate will be low if the two inputs are 11. The Truth Table of NAND gate is shown

Arithmetic/geometric sequences and binomial expansion, find s10 for the ari...

find s10 for the arithmetic sequenxe inwhich a1=5 and a10=68

Linear Equations, y= -3x tell if it is linear or not. our teacher wants it ...

y= -3x tell if it is linear or not. our teacher wants it graphed or something.

#title applications of vector and scalar , #question application of vector ...

#question application of vector and scalar in our daily life

Math, A screening test for a newly discovered disease is being evaluated. I...

A screening test for a newly discovered disease is being evaluated. In order to determine the effectiveness of the new test, it was administered to 900 workers; 150 of the individu

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