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

If tana+sina=m and tana-sina=n, If tanA+sinA=m and tanA-sinA=n, show that m...

If tanA+sinA=m and tanA-sinA=n, show that m 2 -n 2 = 4√mn Ans:    TanA + SinA = m       TanA - SinA = n. m 2 -n 2 =4√mn . m 2 -n 2 = (TanA + SinA) 2 -(TanA - SinA) 2

Homogeneous system , Provided a homogeneous system of equations (2), we wil...

Provided a homogeneous system of equations (2), we will have one of the two probabilities for the number of solutions. 1.   Accurately one solution, the trivial solution 2.

Intercepts, The last topic that we want to discuss in this section is that ...

The last topic that we want to discuss in this section is that of intercepts.  Notice that the graph in the above instance crosses the x-axis in two places & the y-axis in one plac

Linear differential equations, A linear differential equation is of differe...

A linear differential equation is of differential equation which can be written in the subsequent form. a n (t) y (n) (t) + a n-1 (t) y (n-1) (t)+..............+ a 1 (t) y'(

Simplify Radicals, Can I have simplify radicals for Alebgera 2

Can I have simplify radicals for Alebgera 2

How many points did he score during his senior year, Michael scored 260 poi...

Michael scored 260 points during his junior year on the school basketball team. He scored 20% more points during his senior year. How many points did he score during his senior yea

How does a child think-knowing your maths learner, HOW DOES A CHILD THINK? ...

HOW DOES A CHILD THINK? :  You must have interacted with children of various ages. From your experience, do you feel that children start learning, from a very early age, and conti

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