hw13 - 2 Hint: The gradient vector n ( x, y, z ) = 2 rx ˆ...

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Math 454 Problem Set #13 Fall 2008 Sect. 1 Due Thursday, 12/4, at the beginning of class. Reminder. You are encouraged to work together on homework problems. However, the final write- up must be your own. You will be quizzed on some of these problems, so be sure you can do all the problems without help. Read: Ch. 8.4, 9.0, 9.2-3 Problems - Sect. 8.2 #5, 6, 11, 12 - Sect. 8.4 #1 1 , 2 - Sect. 9.2 #1, 2 2 1 “Infinite-period” means the same thing as“saddle-node on invariant circle.” See Sect. 8.4 of the text.
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Unformatted text preview: 2 Hint: The gradient vector n ( x, y, z ) = 2 rx ˆ i + 2 σy ˆ j + 2 σ ( z-2 r ) ˆ k (1) is normal to the ellipsoid at the point ( x, y, z ) and points outward . The ellipsoid will be trapping if the dot product n ( x, y, z ) · f ( x, y, z ) < for all ( x, y, z ) on the ellipsoid, where f is the Lorenz vector field. See also the hint in the back of the book....
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This note was uploaded on 02/17/2010 for the course MATH 142532 taught by Professor Glasner during the Spring '10 term at Arizona.

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