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

Optimization, Optimization : In this section we will learn optimization p...

Optimization : In this section we will learn optimization problems.  In optimization problems we will see for the largest value or the smallest value which a function can take.

Determine radicals in exponent form, Evaluate following.               ...

Evaluate following.                √16 and Solution To evaluate these first we will convert them to exponent form and then evaluate that since we already know how to

Formulas for the volume of this solid, Formulas for the volume of this soli...

Formulas for the volume of this solid V = ∫ b a A ( x) dx          V = ∫ d c A ( y ) dy where, A ( x ) & A ( y ) is the cross-sectional area of the solid. There are seve

Math on a spot, compare: 643,251: 633,512: 633,893. The answer is 633,512.

compare: 643,251: 633,512: 633,893. The answer is 633,512.

Maths for fun-mathematics- in our lives, Maths For Fun :  Often, when I ha...

Maths For Fun :  Often, when I have time on my hands, I try to solve interesting mathematical questions of the following kind. Sometimes my friends and I create the problems, and

Statewide mortality rates, Assume that between workers exposed to asbestos ...

Assume that between workers exposed to asbestos in a shipyard in 1980, 33 died over a 10 year period from COPD, whereas only 24 such deaths would be expected based on statewide mor

Rectilinear figures, Q1- different types of rectilinear figures? Q2- interi...

Q1- different types of rectilinear figures? Q2- interior and exterior angles of the polygon? Q3-relation between interior and exterior angles of polygons? Q4- properties of any fiv

Young entrepreneur, As a creative and innovative entrepreneur, we are requi...

As a creative and innovative entrepreneur, we are required to invent or improvise a product or service that benefits the society and the economy, so what do you think is it?

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