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

.fractions, what is the difference between North America''s part of the tot...

what is the difference between North America''s part of the total population and Africa''s part

Fractions, which fractions is equivalent to 5/ 6 a.20/24 b.9/10 c.8/18 d....

which fractions is equivalent to 5/ 6 a.20/24 b.9/10 c.8/18 d.10/15

Linear functions, Linear functions are of the form: y = a 0 ...

Linear functions are of the form: y = a 0 + a 1 x 1 + a 2 x 2 + ..... + a n x n where a 0 , a 1 , a 2 ..... a n are constants and x 1 , x 2 ..... x n a

Each child is unique in learning development, Each Child Is Unique :  Alth...

Each Child Is Unique :  Although every child goes through similar stages of development, the process may vary from one set of children to another, and also from one child to anoth

What is polygon, What is polygon? A polygon is a shape with three or mo...

What is polygon? A polygon is a shape with three or more sides, in which each side touches another only at its endpoints. Some polygons that you are probably already familiar w

How much money does she have left, Mary has $2 in her pocket. She does yard...

Mary has $2 in her pocket. She does yard work for four various neighbors and earns $3 per yard. She then spends $2 on a soda. How much money does she have left? This translates

speed of the truck , A man travels 600km partly by train and partly by tru...

A man travels 600km partly by train and partly by truck. If he  covers 120km by train and the rest by truck, it takes him eight hours. But, if he travels 200km by train and the res

Find the probability , 1.  What is the probability that the two beverages w...

1.  What is the probability that the two beverages will be of the same kind? 2.  What is the probability that the two beverages will be different? 3.  What is the probability

Inverse laplace transforms, Determining the Laplace transform of a function...

Determining the Laplace transform of a function is not terribly hard if we've found a table of transforms opposite us to use as we saw in the previous section. What we would want t

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