1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Solving for a fixed point for a sine map

  1. Feb 5, 2010 #1
    1. The problem statement, all variables and given/known data
    Consider the sine map x{sub t+1} = f(x{sub t}) where f(x) = r*sin(x*pi).

    For r > 1/pi there are two fixed points, one at the origin that is unstable, and one elsewhere on the curve. The non-origin fixed point starts out, as you turn r just slightly above 1/pi, as stable, but at some point becomes unstable.

    I want to find the value of r at which the second fixed point becomes unstable.

    2. Relevant equations

    3. The attempt at a solution

    To do that, I need to solve x = r*sin(x*pi) for x. How can I do that, or, how else can I find, numerically, the value of r at which the second fixed point becomes unstable?
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted