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

Describe independent events in maths, Describe Independent Events in maths?...

Describe Independent Events in maths? Events are independent if the outcome of one event does not affect the outcome of the second event. If A represents one independent event

How do you find the second minimum spanning tree of a graph, How do you fin...

How do you find the second minimum spanning tree of a graph?  Find the second minimum spanning tree of the following graph.  Ans: The second minimum spanning tree is acq

In how many years is the population expected to be 42, The population of a ...

The population of a particular city is increasing at a rate proportional to its size. It follows the function P(t) = 1 + ke 0.1t where k is a constant and t is the time in years.

Design a game strategy involves process of learning maths, Doing these sums...

Doing these sums initially in this way helps children see why they carry over numbers to the next column. You may like to devise some related activities now. , EI) Give activ

Profit and loss, A man sold an item for Rs 6,750 at a loss 25%. What will b...

A man sold an item for Rs 6,750 at a loss 25%. What will be the selling price of same item if he sells it at a profit of 15%?

Ratio and proportion, find the ratio of each of the following in simplest f...

find the ratio of each of the following in simplest form 1] 9 months to 7 by 4

Michael has 16 cds how many cds does kathleen have, Michael has 16 CDs. Th...

Michael has 16 CDs. This is four more than twice the amount that Kathleen has. How many CDs does Kathleen have? Let x = the number of CDs Kathleen has. Four more than twice th

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