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

Conclude the values of the six trigonometric functions, Conclude the values...

Conclude the values of the six trigonometric functions: Conclude the values of the six trigonometric functions of an angle formed through the x-axis and a line connecting the

Binomial mathematical properties, Binomial Mathematical Properties 1. ...

Binomial Mathematical Properties 1. The expected or mean value = n × p = np Whereas; n = Sample Size p = Probability of success 2. The variance = npq Whereas; q =

Two circles touch each other externally, Two circles touch each other exter...

Two circles touch each other externally: Given: Two circles with respective centres C1 and C2 touch each other externaly at the point P. T is any point on the common tangent

Rational expressions, Now we have to look at rational expressions. A ration...

Now we have to look at rational expressions. A rational expression is a fraction wherein the numerator and/or the denominator are polynomials.  Here are some examples of rational e

Theory of equations, If p,q,r are roots of x^3-3x^2+4x-7=0 (p+2)(q+2)(...

If p,q,r are roots of x^3-3x^2+4x-7=0 (p+2)(q+2)(r+2)=

Mean is 8.32 find the median, In a frequency distribution mode is 7.88, mea...

In a frequency distribution mode is 7.88, mean is 8.32 find the median.  (Ans: 8.17) Ans:  Mode = 3 median - 2 mean 7.88 = 3 median - 2 x 8.32 7.88 +16.64 = 3 median

Calculate how much ribbon is needed to wrap the box, Ribbon is wrapped arou...

Ribbon is wrapped around a rectangular box that is 10 by 8 by 4 in. Using the example provided, calculate how much ribbon is needed to wrap the box. consider the amount of ribbon d

Ratio math help, Mr.Tanaka has 56 students in his choir the ratio of boys ...

Mr.Tanaka has 56 students in his choir the ratio of boys to girls is 3:4 how many boys and girls are in his class

Calculate the area of remaining piece of cardboard, A piece of cardboard in...

A piece of cardboard in the shape of a trapezium ABCD & AB || DE, ∠ BCD = 900, quarter circle BFEC is removed. Given AB = BC = 3.5 cm, DE = 2 cm. Calculate the area of remaining p

Surface area with parametric equations, Surface Area with Parametric Equati...

Surface Area with Parametric Equations In this final section of looking at calculus applications with parametric equations we will take a look at determining the surface area o

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