Statistical analysis of the first digits of the binary expansion of Feigenbaum constants \(\alpha\) and \(\delta\)

DOI10.1016/j.jfranklin.2004.11.004zbMath1088.37015OpenAlexW1536979440MaRDI QIDQ1776670

Niranjan Chakravarthy

Publication date: 12 May 2005

Published in: Journal of the Franklin Institute (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfranklin.2004.11.004

zbMATH Keywords

logistic mapbifurcation diagramrandomnessperiod doublingsymbolic sequencesglidingnonnormal binary numbers

Mathematics Subject Classification ID

Symbolic dynamics (37B10) Iteration of real functions in one variable (26A18) Dynamical systems involving maps of the interval (37E05) Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items (3)

On the statistical analysis of Feigenbaum constants ⋮ Addendum: On the statistical analysis of the first digits of the Feigenbaum constants ⋮ Structure of the correlation function at the accumulation points of the logistic map

Cites Work

• The universal metric properties of nonlinear transformations
• Is \(\pi\) normal ?
• Toward a quantitative theory of self-generated complexity
• Symbolic dynamics and entropy analysis of Feigenbaum limit sets
• Algebraic irrational binary numbers cannot be fixed points of non-trivial constant length or primitive morphisms
• Toward a probabilistic approach to complex systems
• The quest for pi
• Transcendence of numbers with a low complexity expansion
• Quantitative universality for a class of nonlinear transformations
• On finite limit sets for transformations on the unit interval
• Parallel integer relation detection: Techniques and applications
• Ramanujan, Modular Equations, and Approximations to Pi or How to Compute One Billion Digits of Pi
• A Precise Calculation of the Feigenbaum Constants
• Entropy analysis of substitutive sequences revisited
• The Construction of Decimals Normal in the Scale of Ten
• Analytic Solutions of the Cvitanović–Feigenbaum and Feigenbaum–Kadanoff–Shenker Equations
• FROM SYMBOLIC DYNAMICS TO A DIGITAL APPROACH
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