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Unformatted text preview: B ( x, y ) = e-2 x . What restrictions does Dulacs criterion (Thm 4.1.2 of the text by Wiggins) place on the existence of periodic orbits for this system? 3. (20 pts total) Suppose x = x (4) y =-y + xy + x 2 (5) (a) (5 pts) What is the stable eigenspace E s and the unstable eigenspace E u for the xed point at the origin? (b) (10 pts) Find the approximation y = h ( x ) for the local unstable manifold W u loc of the origin accurate to O ( x 3 ). (c) (5 pts) What is the stable manifold W s of the origin? 1...
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- Fall '08