Symbol-To-Symbol Correlation Function At The Feigenbaum Point Of The Logistic Map
Abstract
Recently, Simple Dynamical Systems Such As The 1-D Maps On The Interval, Gained Significant Attention In The Context Of Statistical Physics And Complex Systems. The Decay Of Correlations In These Systems, Can Be Characterized And Measured By Correlation Functions. In The Context Of Symbolic Dynamics Of The Nonchaotic Multifractal Attractors (I.e. Feigenbaum Attractors), One Observable, The Symbol-To-Symbol Correlation Function, For The Generating Partition Of The Logistic Map, Is Rigorously Introduced And Checked By Numerical Experiments. Thanks To The Metropolis-Stein-Stein (MSS) Algorithm, This Observable Can Be Calculated Analytically, Giving Predictions In Absolute Accordance With Numerical Computations. The Deep, Algorithmic Structure Of The Observable Is Revealed Clearly Reflecting The Complexity Of The Multifractal Attractor. © World Scientific Publishing Company.
Recommended Citation
K. Karamanos et al., "Symbol-To-Symbol Correlation Function At The Feigenbaum Point Of The Logistic Map," International Journal of Bifurcation and Chaos, vol. 23, no. 7, article no. 1350118, World Scientific Publishing, Jan 2013.
The definitive version is available at https://doi.org/10.1142/S0218127413501186
Department(s)
Physics
Keywords and Phrases
Correlation function; Feigenbaum attractors; logistic map; symbolic dynamics
International Standard Serial Number (ISSN)
0218-1274
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2024 World Scientific Publishing, All rights reserved.
Publication Date
01 Jan 2013
