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Linearly stable / non-linearly unstable map example

  1. Apr 6, 2017 #1
    1. The problem statement, all variables and given/known data

    Give examples of fixed points of vector fields and maps that are stable in the linear approximation but are nonlinearly unstable

    2. Relevant equations


    3. The attempt at a solution

    I was able to find an example in a vector field that, when the Jacobian is found and the fixed point at the origin is analyzed, gives eigenvectors of +/- i, indicating Lyapunov stability but not asymptotic stability. When this equation is converted to polar coordinates, it is show clearly that the r' = r^3 and so the graph actually spirals away from the origin.

    However, I have been unsuccessful in finding a map version of this. I am taking a few stabs in the dark and they don't seem to be getting me anywhere, and I'm not sure how to go about constructing the answer...

    Thanks for any and all help!
     
  2. jcsd
  3. Apr 11, 2017 #2
    Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.
     
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