Entropy Measures as Geometrical Tools in the Study of Cosmology.

Classical chaos is often characterized as exponential divergence of nearby trajectories. In many interesting cases these trajectories can be identified with geodesic curves. We define here the entropy by S = ln χ ( x ) with χ ( x ) being the distance between two nearby geodesics.

Heart Rate Variability Density Analysis (Dyx) and Prediction of Long-Term Mortality after Acute Myocardial Infarction.

Aims: The density HRV parameter Dyx is a new heart rate variability (HRV) measure based on multipole analysis of the Poincaré plot obtained from RR interval time series, deriving information from both the time and frequency domain. Preliminary results have suggested that the parameter may provide new predictive information on mortality in survivors of acute myocardial infarction (MI). This study compares the prognostic significance of Dyx to that of traditional linear and nonlinear measures of HRV.

Geometry of Hamiltonian chaos.

The characterization of chaotic Hamiltonian systems in terms of the curvature associated with a Riemannian metric tensor in the structure of the Hamiltonian is extended to a wide class of potential models of standard form through definition of a conformal metric. The geodesic equations reproduce the Hamilton equations of the original potential model when a transition is made to an associated manifold. We find, in this way, a direct geometrical description of the time development of a Hamiltonian potential model.