Math 485 10 March 11 Page 1 of 8 Mar 10 2011 Math 485 10 March 11 Page 2 of 8 Mar 10 2011 Math 485 10 March 11 Page 3 of 8 Mar 10 2011 Stability of xed points 1 nd the xed points 2 stability of xed point Similar to a center x0 is a stable xed point if for any small neighborhood of x0 U x0 there exists another neighborhood of x0 V x0 such that Similar to a sink Math 485 10 March 11 Page 4 of 8 Mar 10 2011 Fixed points where f x intersects y x Math 485 10 March 11 Page 5 of 8 Mar 10 2011 To be unstable needs to be going out but also needs to go to in nity if there is a limiting value then it is stable Math 485 10 March 11 Page 6 of 8 Mar 10 2011 How to nd orbit Periodic orbit of period n Claim if f has periodic orbit of period 3 then f has periodic orbit of any period Math 485 10 March 11 Page 7 of 8 Mar 10 2011 An orbit with period 2 also has period 4 and 8 Math 485 10 March 11 Page 8 of 8 Mar 10 2011
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