1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    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!

Bifurcations in maps

  1. May 16, 2012 #1
    1. The problem statement, all variables and given/known data
    Prove carefully that the following map has a horseshoe for one positive value of [itex]\mu[/itex]
    xn+1 = xn2 - [itex]\mu[/itex]
    For what positive values of [itex]\mu[/itex] will the map have a horseshoe?
    2. Relevant equations



    3. The attempt at a solution
    xn+1 = xn2 - [itex]\mu[/itex] = g(xn,[itex]\mu[/itex])
    ∂g/∂x = 2x
    → turning pt at 2x = 0 → turning pt at x=0

    Intersects the x axis at 0 = x2 - [itex]\mu[/itex]
    x = ±√[itex]\mu[/itex]

    I am not even sure if I am on the right track at all. It feels very wrong so any help would be greatly appreciated
     
  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



Similar Discussions: Bifurcations in maps
  1. Bifurcation Diagrams (Replies: 1)

  2. Bifurcation question (Replies: 2)

Loading...