Discrete Dynamics in Nature and Society
Volume 2 (1998), Issue 3, Pages 187-194
doi:10.1155/S1026022698000168
Symbolic dynamics, entropy and complexity of the Feigenbaum map at the accumulation point
Werner Ebeling1
and Katja Rateischak2
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
Abstract
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.