Stefano Isola
Renewal sequences and intermittency
(38K, Plain-TeX)

ABSTRACT.  In this paper we examine the generating function $\Phi (z)$ 
of a renewal sequence arising from the distribution of return times 
in the `turbulent' region for a class of piecewise 
affine interval maps introduced by Gaspard and Wang$^{(1)}$ 
and studied by several authors$^{(2-8)}$. 
We prove that it admits a meromorphic continuation to the entire 
complex $z$-plane with a branch cut along the ray $(1,+\infty )$. 
Moreover we compute the asymptotic behaviour of the coefficients 
of its Taylor expansion at $z=0$. 
From this, the exact polynomial asympotics for the rate of mixing 
when the invariant measure is finite and of 
the scaling rate when it is infinite are obtained.