Standard deviation of recurrence times for piecewise linear transformations

This paper is concerned with dynamical systems of the form (X,f) where X is a bounded interval and f comes from a class of measure-preserving, piecewise linear transformations on X. If A⊆X is a Borel set and x∈A, the Poincaré recurrence time of x relative to A is defined to be the minimum of {n:n∈Nandfn(x)∈A}, if the minimum exists, and ∞ otherwise. The mean of the recurrence time is finite and is given by Kac\u27s recurrence formula. In general, the standard deviation of the recurrence times need not be finite but, for the systems considered here, a bound for the standard deviation is derived