Whether the following statemant is correct (I guess the answer is "Yes" and I guess that maybe it is trivial for an expert about Pseudo-Anosov map)? 


"For a given $n\in N$, there exists a closed orientbale surface $\Sigma^n$ such that there exists a pseudo-Anosov diffeomorphism 
$f\_n$ on $\Sigma^n$ with an $n$-prong singularity. "


Could you pleae provide me some references or comments? Thank you.



Pseudo-Anosov map with n-prong singularity
The answer to your question is yes and essentially the only restriction on the singularity type (=number of prongs) is the one coming from Euler-Poincare formula. For further details, I think an useful reference is, e.g., the book "A Primer on Mapping Class Groups" by B. Farb and D. Margalit (<http://press.princeton.edu/titles/9495.html>).


