# A Lyapunov coefficient for function f(x) = 1/(1+x)

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1. May 16, 2017

### Sasho Andonov

May I use function f(x) = 1/(1+x) to investigate chaos?
I am trying to understand chaos using this function, but things are not going as I expected....
Could you please advice me how I can calculate Lyapunov coefficient for this function?

2. May 21, 2017

### PF_Help_Bot

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.

3. May 31, 2017

### Anachronist

It isn't clear how you intend to use this function. Are you using it to iterate something? Are you using it as a mapping function somehow?

As an iteration $x_{i+1} = \frac{1}{1+x_i}$, it converges to $\frac{\sqrt{5}-1}{2}$, which is the Golden Ratio minus 1. The Golden Ratio crops up a lot in chaos theory. To calculate a meaningful Lyapunov Exponent, you would need some sort of chaotic time series. Because this function converges, the Lyapunov Exponent would always be negative.