 98670 Stefano Isola
 Renewal sequences and intermittency
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Oct 22, 98

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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$^{(28)}$.
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.
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