Finally it seems that it's difficult to use Adobe Illustrator correctly (you need to fix the line width to avoid to use the current line width). So I propose to draw the picture only with TikZ.
Remark : I use a tikzpicture inside a tikzpicture intentionally. If you fix line width =1pt in the first tikzpicture, the current line width in the second one is 0.4pt.
\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{arrows}
\begin{document}
\newcommand{\midarrow}{\tikz \draw[-stealth'] (0,0) -- +(.1,0);}
\newcommand{\revmidarrow}{\tikz \draw[-stealth' reversed] (0,0) -- +(.1,0);}
\begin{tikzpicture}
\node (A) at (0,0) {%
\begin{tikzpicture}
\draw circle[radius=2];
\begin{scope}[line width = 1pt]
\draw (-120:2) .. controls (-150:0.25) .. (-180:2) node[pos=.8,sloped,scale=2] {\revmidarrow};
\draw (0:2) .. controls (-30:0.25) .. (-60:2) node[pos=.8,sloped,scale=2] {\midarrow};
\draw (120:2) .. controls (160:.75) and (180:.5) .. (0:0)
.. controls (0:.5) and (20:.75) .. (60:2)
node [pos=.8,sloped,scale=2] {\midarrow};
\end{scope}
\end{tikzpicture}
};
\end{tikzpicture}
\end{document}

[scale=2.7]? In your example, the scaling do nothing ! – Alain Matthes Jul 02 '12 at 15:07pdftk– Jul 02 '12 at 16:581 wat the beginning of the stream corrects this error. – Paul Gaborit Jul 04 '12 at 00:29