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2icy x 8(x1-x)y4y? - = + y I((x - - - 8(-x1 - x)yty? ...

2icy x 8(x1-x)y4y? - = + y I((x - - - 8(-x1 - x)yty? + [(x + x1)2 - y = y2 x2 + - ((x - x1)2 + y? - y2) y [(x - x1)2 + (y - y1) ²) ((x - x1)2 + (y + y )²)]³/² - y2) + I((x + x1² + (y - y1) ² ((x + x12 + (y + y1)²)]3/2 1) Write the system of four 1...

2. (a) A dynamical written canonical form gives as SY/ with...

2. (a) A dynamical written canonical form gives as SY/ with (:) and k # real constant Identify the type and stability of the critical point at the origin, depending on all possible values giving the ranges values of for which they occur. Justify your ariswer. (b) Consider the dynamical system ...

6. Describe the phase portrait of the map of the circle give...

6. Describe the phase portrait of the map of the circle given by f(θ) = θ + 2π/n + ϵ sin(n θ) for 0 < ϵ < 1/n. 7. Prove that a homeomorphism of R can have no periodic points with prime period greater than 2. Give an example of a homeomorphism that has a perio...

1. Determine for what values of lambda, f(x) = lambda x (1-x...

1. Determine for what values of lambda, f(x) = lambda x (1-x) has an attracting fixed point p. (See the cheat-sheet on piazza for definitions). For those parameters lambda, what are the intervals containing p on which f is a uniform contraction? 2. Let f(x) = 2 x (1-x). Graph f¹°(x) on [1/...

Find the general solution of the following DISCRETE dynamica...

Find the general solution of the following DISCRETE dynamical systems and then find the particular solution for the given initial conditions. State the nature and location of the singular point. 1.) X(n+1) = [ 2 1 -1; 0 -1 2; 0 0 -1] * X(n) ; with X(0) = [ 1 2 -3 ] T 2.) X(n+1) = [ 12 -15; 4 -...

3. Satellites spin so as to keep a fixed axis; this is espec...

3. Satellites spin so as to keep a fixed axis; this is especially important in maintaining communication with ground stations as antennas and dishes have to point in a single consistent direction. A question that needs to be asked is: is it better to have short, "fat" satellites...

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