Bachelor's degree final project: Approximations of invariant curves of diffeomorphisms

What is the utility of the current library ?

Assumes that we have a discret system like that:

$\begin{cases} \bar x = f(x, \theta) + \varepsilon g(x,\theta)\\ \bar \theta = \theta + \omega, \end{cases}$

where $ f, g $ are differential maps with the second variable on the torus.

A continuous map $x\colon \mathbb{T} \rightarrow \mathbb{R}$ is an invariant curve of the discret system if, and only if,

$x(\theta + \omega) = f(x(\theta), \theta) + \varepsilon g(x(\theta),\theta) \quad \text{ for all } \theta.$

The value $\omega$ is known as the rotation number of the curve and it is common to suppose that is a irrational real number.

The library compute an approximation of some invariant curve of the discret system.