Hellow @Krisztian_Kosi. I am really glad that you want to check out this package and even maybe contribute something!
Since the date of the first post in this topic, the package has evolved greatly and has at least 10 times more content!
You can find the documentation for the package here: Introduction · DynamicalSystems.jl
I am working non-stop on this package. Currently I am trying to implement a method that finds unstable periodic orbits of any map and of any order (you cannot see this in the documentation yet).
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I just quickly run through the documentation. Man, it’s huge! It will be a huge help in classical approach of nonlinear systems (basically what is in Slotin’s book). Keep up this good work.
I think this classical Lyapunov based methods will be with us for a while. It’s not so common, that someone interested in nonlinear systems and using nonlinear methods. In the industry the linear control (and PID) is “THE CONTROL”. The simple reason is, that the engineers can’t use math, and they stacked in linear control. Any work with is help to make this phenomena easier is a step to forget linear control.
The classical approach, with this library, is a huge step.
Because, they don’t need to change to much in the ideas, just a bit complicated. And that library helps them to do this step.
I had an interesting experience. I can teach nonlinear control with RFPT in BSc levels, but Professors can’t see the beauty in it (expect some math Professors in my department).
The prep work isn’t too difficult. I used Lorenz system just an abstract nonlinear MIMO system. I added control signals, and try to tune up the controller.
The math, which is needed to use this controller, and understand some of the behaviour the controller, is simple. I teach in Calculus I classes. 
If you have some free time, you can play with it. I just roughly sketch the RFPT with Lorenz System. (sorry if I made a mistake in the sketch).
Unfortunately I have 0 experience with control theory so I cannot understand the script without doing some studying. But it seems to work fine 
I am quite honoured that you found the package so great! If you want, you can join the gitter channel here: JuliaDynamics/Lobby - Gitter and you can also invite other people that may be interested there!