- #1

MathAmateur

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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

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?

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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