Discrete Dynamics in Nature and Society
Volume 2 (1998), Issue 3, Pages 187-194

Symbolic dynamics, entropy and complexity of the feigenbaum map at the accumulation point

Werner Ebelings1 and Katja Rateitschak2

1Institute of Physics, Humboldt University Berlin, Invaliden Str. 110, Berlin D-lOll5, Germany
2Center for Nonlinear Phenomena and Complex Systems, Free University of Brussels, Brussels B-1050, Belgium

Received 14 February 1998

Copyright © 1998 Werner Ebelings and Katja Rateitschak. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper aims to make further contributions to the exploration of the symbolic dynamics generated by the logistic map at Feigenbaum accumulation point. In particular we are interested in the grammar of these sequences; completing earlier studies we study here arbitrary partitions also. Our main aim is the investigation of the special grammars which characterize the long-range correlations between letters. Considering these sequences as standard examples of a complex system, we introduce and discuss a complexity function derived from the conditional entropies. Further we discuss local predictabilities.