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.