This study focuses on the dynamic pattern of heart rate variability in the frequency range of respiration, the so-called respiratory sinus arrhythmia. Forty experimental time series of heart rate data from four healthy adult volunteers undergoing a paced respiration protocol were used as an empirical basis. For pacing-cycle lengths >8 s, the heartbeat intervals are shown to obey a rule that can be expressed by a one-dimensional circle map (next-angle map). Circle maps are introduced as a new type of model for time series analyses to characterize the nonlinear dynamic pattern underlying the respiratory sinus arrhythmia during voluntary paced respiration. Although these maps are not chaotic, the dynamic pattern shows typical imprints of nonlinearity. By starting from a piecewise linear model, which describes the different circle maps obtained from the empirical time series for various pacing frequencies, time invariant measures can be introduced that characterize the dynamic pattern of heart rate variability during voluntary slow-paced respiration.