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

Conclusion of egroff''s theorem and lusin''s theorem, (1) Show that the con...

(1) Show that the conclusion of Egroff's theorem can fail if the measure of the domain E is not finite. (2) Extend the Lusin's Theorem to the case when the measure of the domain E

Find the value of p and q for which the system of equations, Find the value...

Find the value of p and q for which the system of equations represent coincident lines 2x +3y = 7, (p+q+1)x +(p+2q+2)y = 4(p+q)+1 Ans: a 1  = 2, b 1 = 3, c 1 = 7 a 2  =

Find the root, (a) Convert z  = - 2 - 2 i to polar form. (b) Find ...

(a) Convert z  = - 2 - 2 i to polar form. (b) Find all the roots of the equation w 3 = - 2 - 2 i . Plot the solutions on an Argand diagram.

Find how much more space than the toy it will cover, A Solid toy in the for...

A Solid toy in the form of a hemisphere surmounted by the right circular cone of height  2cm  and  diameter  of  the  base  4  cm .If  a right  circular  cylinder circumscribes the

Determine the centralizer and the order of the conjugacy, Determine the cen...

Determine the centralizer and the order of the conjugacy: 1)      Determine the centralizer and the order of the conjugacy class of the matrix [1, 1; 0, 1] in Gl­ 2 (F 3 ).

The achievements from math, i love math..but i am afraid to study it... i m...

i love math..but i am afraid to study it... i mean i ma afraid that it may leave me in clay...what can you suggest me?

Indices, what are the advantages and disadvantages of both Laspeyres and Pa...

what are the advantages and disadvantages of both Laspeyres and Paasche index

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