98-670 Stefano Isola

Renewal sequences and intermittency (38K, Plain-TeX) 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$^{(2-8)}$. 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.

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