In the intro of the movie "Pi: faith in chaos" appear many mathematical elements that I recognize like Möbius band. But this one I don't get it:
Obviously is a surface in the space, but what is its name? by the direction arrows and using the terminology of dynamical system I guess is used as attractor.
As John Douma pointed out in a comment, a clue can be found in note c of the English Wikipedia page for the film:
A version of that famous text can be viewed in the Internet Archive, and here is a direct link to the page (75) with (the negative of) the image in question.
The text clarifies that it is a relief (showing the magnitude) of the complete elliptic integral of the first kind $K(k)=\displaystyle{\int_0^{\pi/2}\frac{\mathrm d\theta}{\sqrt{1-k^2\sin^2\theta }}}$ as a function of $\lambda=k^2$. A closely-related image, but for it as a function of $k$, can be found at the MathWorld page for the function.