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This paper introduces a novel methodology able to provide time varying estimates of the Lyapunov Spectrum within a point process framework. The algorithm is applied to ECG-derived data to characterize heartbeat nonlinear dynamics by using a cubic autoregressive point process model. Estimation of the model parameters is ensured by the Laguerre expansion of the Wiener-Volterra kernels along with a maximum local log-likelihood procedure. In addition to the instantaneous Lyapunov exponents, as well as indices related to higher order dynamic polyspectra, our method is also able to provide all the instantaneous time domain and frequency domain measures of instantaneous heart rate (HR) and heart rate variability (HRV) previously considered. Experimental results show that our method is able to track complex cardiovascular control dynamics during fast transitional gravitational changes.