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

Developing an understanding of subtraction, DEVELOPING AN UNDERSTANDING O...

DEVELOPING AN UNDERSTANDING OF SUBTRACTION :  The process of subtraction is the reverse of that of addition. Adding more to a collection to make it bigger is just the reverse

Explain peano''s axioms with suitable example, Question 1 Explain Peano's ...

Question 1 Explain Peano's Axioms with suitable example Question 2 Let A = B = C= R, and let f: A→ B, g: B→ C be defined by f(a) = a+1 and g(b) = b 2 +1. Find a) (f °g

Fact of the wronskian method, Given two functions f(x) and g(x) which are d...

Given two functions f(x) and g(x) which are differentiable on some interval I  (1) If W (f,g) (x 0 ) ≠ 0 for some x 0 in I, so f(x) and g(x) are linearly independent on the int

Express the statement as a disjunction in dnf, State the following statemen...

State the following statement as a disjunction (in DNF) as well using quantifiers:      There does not exit a woman who has taken a flight on each airline in the world.

Fraction, give some examples of fractions that are already reduce

give some examples of fractions that are already reduce

.fractions, what is the difference between North America''s part of the tot...

what is the difference between North America''s part of the total population and Africa''s part

Word problems, A baseball card was worth $5.00 in 1940. It doubled in value...

A baseball card was worth $5.00 in 1940. It doubled in value every decade. How much was it worth in 2000?

Unitary Method Sample Questions, Where can I find sample questions of Unita...

Where can I find sample questions of Unitary Method for kids to practice? I need  Unitary Method  study material if availbale here on website, i found there is very useful material

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