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

What difference among the areas of the two sections of a, If the areas of t...

If the areas of two sections of a garden are 6a + 2 and 5a, what is the difference among the areas of the two sections within terms of a? Because the question asks for the diff

The arithmetic mean, Arithmetic mean Arithmetic means is commonly know...

Arithmetic mean Arithmetic means is commonly known as average or mean it is acquired by first of all summing up the values provided and by dividing the total value by the tota

two women may stand behind each othe, How many ways can six men and three ...

How many ways can six men and three women form a line if no two women may stand behind each other?

What is angle pairs, What is Angle Pairs? Two angles are adjacent angle...

What is Angle Pairs? Two angles are adjacent angles if they have the same vertex and share one side. Vertical angles are a pair of nonadjacent angles formed by two intersecting

.gradient, Draw the graph of y=x^2-4x from x=-1 to x=5.use the scale of 2cm...

Draw the graph of y=x^2-4x from x=-1 to x=5.use the scale of 2cm on the x axis and 1cm on the y axis.Estimate the gradient at point:x=4, x=2 and x=0

Detremine the surface area to the nearest inch, If a tabletop has a diamete...

If a tabletop has a diameter of 42 in, Detremine the surface area to the nearest inch? (π = 3.14) a. 1,384 in 2 b. 1,319 in 2 c. 1,385 in 2 d. 5,539 in 2 c. Th

Write algorithm for the multiplication of a 3-digit number, E1) Why do we s...

E1) Why do we shift the place by one, of the result in the second row of the calculation, when we multiply, say, 35 by 237 E2) Write down the algorithm for the multiplication of

Maximin method -decision making under uncertainty, Decision making under un...

Decision making under uncertainty Various methods are used to make decision in circumstances whereas only the pay offs are identified and the likelihood of every state of natur

Rules of integration, Rules of Integration 1. If ...

Rules of Integration 1. If 'k' is a constant then ∫Kdx =  kx + c 2. In

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