402_502_W11_hw7 - o± 1 say what should the dynamics o±...

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AMATH 402/502 Homework DUE at time and place posted on website 1 Consider the 2-D linear map x n +1 = Ax n , where A = p 0 1 / 2 - 1 / 2 a P a. Find the fxed point(s) ±or any value o± the real parameter a . b. Say whether each fxed point(s) is stable or unstable when a = 1. Show your work. c. Repeat ±or a = 2 . 2 Problem 8.7.2. 3 Problem 8.7.3. Here, the key in connecting with the viewpoint we took in class is to frst “trans±orm” the time-dependent system in 1-D into a time-independent system on the cylinder. Make sure you’ve care±ully studied example 8.7.2 o± the textbook. One question you might want to consider in setting this up: i± your cylinder has a fxed circum±erence
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Unformatted text preview: o± 1, say, what should the dynamics o± the “theta” variable be? 4 Problem 10.1.12. Do (d) on a calculator or via simple computer code. No need to turn in anything ±or (d), however. 5 Problem 10.3.2 6 Problem 10.3.5 ALSO: • Problem 10.1.11. Work on this one as practice, but no need to turn anything in. The homework will be graded statistically. Late homework is not accepted. Your homework should be neat and readable (the TA is allowed to subtract points ±or presentation)....
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This note was uploaded on 02/28/2011 for the course AMATH 402 taught by Professor Staff during the Spring '08 term at University of Washington.

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