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Henon Attractor

  • #1
1. Homework Statement

I am studying Henon Attractors. The Henon map is recursively defined as follows:

[tex]x_{t+1} = a - x^2_{t} + by_{t}
y_{t+1} = x_{t}[/tex]

I am supposed to find the fixed point (may be unstable) that is contained with the chaotic behavior



The Attempt at a Solution



It is clear that to find the fixed point would be when [tex] x_{t+1}, x_{t}, y_{t} [/tex]
are all equal (Lets call them all [tex] x_{b} [/tex]). It seemed obvious to just plug in
[tex] x_{b} [/tex] and solve the quadratic, but the book had an extra term in the answer and I do not know where it came from:
[tex] -x^2_{b} + (b-1) x_{b} +a = 0 [/tex]. Where did the -1 in the b-1 term come from?
 
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Answers and Replies

  • #2
311
1
If you just plug in x_b for x_t, y_t, and x_{t+1}, then the equation you get is exactly what the book says. Do your math again.
 
  • #3
Oh, yes, the x_{b} on the left side is subtracted from the right to make it equal to 0. Duh!

Could you now how I insert a new line in the Latex equation? I can't seem to keep those two first equations from running together.
 
  • #4
311
1
Oh, yes, the x_{b} on the left side is subtracted from the right to make it equal to 0. Duh!

Could you now how I insert a new line in the Latex equation? I can't seem to keep those two first equations from running together.
The latex symbol for new line is \\
 
  • #5
I did the following and got the following result:

x_{t+1} = a - x^2_{t} + by_{t} \\
y_{t+1} = x_{t}

[tex]x_{t+1} = a - x^2_{t} + by_{t}\\
y_{t+1} = x_{t}[/tex]
 
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