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

Karamanos, Kostas and Kotsireas, Ilias (2004) Statistical analysis of the first digits of the binary expansion of Feigenbaum constants $\alpha$ and $\delta$. [Preprint]

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      Abstract

      We present a detailed statistical analysis of the blocks appearing in the binary expansions of the Feigenbaum constants $\alpha$ and $\delta$ for the logistic map. Significant deviations from randomness are revealed, suggesting that these constants correspond to non-normal binary numbers. Applying a widely believed conjecture, it is concluded that the transcendental character of the constants can be seriously envisaged, within the limits of the statistical precision corresponding to the number of digits available.

      Item Type: Preprint
      Additional Information: pubdom FALSE
      Uncontrolled Keywords: Logistic map, Experimental mathematics, Feigenbaum constants
      Subjects: 82-xx Statistical mechanics, structure of matter
      Faculty: UNSPECIFIED
      Depositing User: Users 1 not found.
      Date Deposited: 15 Apr 2004
      Last Modified: 21 Apr 2010 11:13
      URI: https://docserver.carma.newcastle.edu.au/id/eprint/258

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