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

[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?

 

[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.