Limit law of rescaled hitting time functions for quadratic irrational rotations

The paper focuses on analyzing the first asymptote of hitting time functions in relation to dynamical partitions. We study the circle maps with quadratic irrational rotations whose continued fractions exhibit eventual periodicity. The main aim of this paper is to establish that the sequence of distribution functions of rescaled hitting times determined by dynamical partitions, converges to finite limit points. Moreover, it is proved that the limit functions of these distribution functions are piecewise linear distribution functions.