hw6 - u being the coordinate along the center eigenspace....

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Applied Dynamical Systems - ME215A Fall 2010 Homework 6 - Due Wednesday November 10 - in class 1. (20 pts total) Consider the vector field ˙ x = y - 3 x 2 + xy, (1) ˙ y = - 3 y + y 2 + x 2 . (2) (a) (5 pts) What are the eigenvalues of the fixed point at the origin? Find a linear coordinate transformation ± x y ! = S ± u v ! (3) so that the linear part of the equations in the new coordinates ( u, v ) is diagonal, with
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Unformatted text preview: u being the coordinate along the center eigenspace. (b) (10 pts) Find the approximation for the center manifold v = h ( u ) of the xed point at ( u, v ) = (0 , 0) accurate to third order in u . (c) (5 pts) Use this to nd the equation u = g ( u ) for the dynamics on the center manifold accurate to fourth order in u . 1...
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This note was uploaded on 12/29/2011 for the course ME 215a taught by Professor Moehlis,j during the Fall '08 term at UCSB.

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