Kolmogorov-Sinai entropy from recurrence times

Abstract

Observing how long a dynamical system takes to return to some state is one of the most simple ways to model and quantify its dynamics from data series. This work proposes two formulas to estimate the KS entropy and a lower bound of it, a sort of Shannon's entropy per unit of time, from the recurrence times of chaotic systems. One formula provides the KS entropy and is more theoretically oriented since one has to measure also the low probable very long returns. The other provides a lower bound for the KS entropy and is more experimentally oriented since one has to measure only the high probable short returns. These formulas are a consequence of the fact that the series of returns do contain the same information of the trajectory that generated it. That suggests that recurrence times might be valuable when making models of complex systems.

References in corpus (4)

• Recurrence Plots for the Analysis of Complex Systems
• Poincare recurrence and measure of hyperbolic and nonhyperbolic chaotic attractors
• The multifractal fly: a dynamically multilayered visual system
• Return time statistics for invariant measures for interval maps with positive Lyapunov exponent

Cited by in corpus (9)

• Recurrence threshold selection for obtaining robust recurrence characteristics in different embedding dimensions
• Trends in recurrence analysis of dynamical systems
• A unified and automated approach to attractor reconstruction
• Successful network inference from time-series data using Mutual Information Rate
• Stickiness and recurrence plots: an entropy-based approach
• Geometric and dynamic perspectives on phase-coherent and noncoherent chaos
• Massive evaluation and analysis of Poincaré recurrences on grids of initial data: a tool to map chaotic diffusion
• Stability analysis of planetary systems via second-order Rényi entropy
• Characterizing and quantifying weak chaos in fractional dynamics