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

An example of build upon the child''s background, What are the other differ...

What are the other differences between learners that a teacher needs to keep in mind, while teaching?  Let us see an example in which a teacher took the pupil's background into acc

Square and square root., the value of square root of 200multiplied by squar...

the value of square root of 200multiplied by square root of 5+

Evaluate integrals (1 - (1 /w) cos (w - ln w) dw, Evaluate following integr...

Evaluate following integrals.                       ( (1 - (1 /w) cos (w - ln w) dw Solution In this case we know how to integrate only a cosine therefore let's makes th

Diffrence between rational and irrational numbers, Q. Diffrence between Rat...

Q. Diffrence between Rational and Irrational Numbers? Ans. A number which is not rational is called irrational. The word "irrational" sounds not quite right...as though th

Algebra, prove That J[i] is an euclidean ring

prove That J[i] is an euclidean ring

Linear graph, in the form of linear graph interpret the ralationship betwee...

in the form of linear graph interpret the ralationship between two quantities

Sums and differences of cubes and other odd powers, Sums and Differences of...

Sums and Differences of Cubes (and other odd powers)? You can factor a sum or difference of cubes using the formulas a 3 - b 3 = (a - b )(a 2 + ab + b 2 ) and a 3 + b 3 =

#Regular Expression, Find the Regular Grammar for the following Regular Exp...

Find the Regular Grammar for the following Regular Expression: a(a+b)*(ab*+ba*)b.

Algebra, let setM={X,2X,4X} for any numberX .if average (arthemetic mean)of...

let setM={X,2X,4X} for any numberX .if average (arthemetic mean)of the number in setM is 14.what is the value of X?

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