Letellier Christophe
CORIA UMR 6614 - Université de Rouen, Avenue de l'Université, Boîte Postale 12, F-76801 Saint-Etienne du Rouvray cedex, France.
Phys Rev Lett. 2006 Jun 30;96(25):254102. doi: 10.1103/PhysRevLett.96.254102. Epub 2006 Jun 29.
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.
递归图最初被引入以量化混沌动力学的递归特性。几年后，递归量化分析被引入，将图形表示转化为统计分析。在引入的不同度量中，发现香农熵与最大李雅普诺夫指数的倒数相关。这里通过使用一个新定义（仍然基于递归图）解决了这与香农熵通常解释之间的差异，并且验证了这个新定义与最大李雅普诺夫指数相关，正如佩辛猜想所预期的那样。还提供了与从符号动力学计算得到的香农熵的比较。
