Estimating the Shannon entropy: recurrence plots versus symbolic dynamics.
Recurrence plots were first introduced to quantify the recurrence properties of chaotic dynamics. A few years later, the recurrence quantification analysis was introduced to transform graphical representations into statistical analysis. Among the different measures introduced, a Shannon entropy was found to be correlated with the inverse of the largest Lyapunov exponent. The discrepancy between this and the usual interpretation of a Shannon entropy is solved here by using a new definition--still based on the recurrence plots--and it is verified that this new definition is correlated with the largest Lyapunov exponent, as expected from the Pesin conjecture. A comparison with a Shannon entropy computed from symbolic dynamics is also provided.
Letellier
Christophe
C
CORIA UMR 6614 - Université de Rouen, Avenue de l'Université, Boîte Postale 12, F-76801 Saint-Etienne du Rouvray cedex, France.