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A006890
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Decimal expansion of Feigenbaum bifurcation velocity.
(Formerly M3264)
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11
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4, 6, 6, 9, 2, 0, 1, 6, 0, 9, 1, 0, 2, 9, 9, 0, 6, 7, 1, 8, 5, 3, 2, 0, 3, 8, 2, 0, 4, 6, 6, 2, 0, 1, 6, 1, 7, 2, 5, 8, 1, 8, 5, 5, 7, 7, 4, 7, 5, 7, 6, 8, 6, 3, 2, 7, 4, 5, 6, 5, 1, 3, 4, 3, 0, 0, 4, 1, 3, 4, 3, 3, 0, 2, 1, 1, 3, 1, 4, 7, 3, 7, 1, 3, 8, 6, 8, 9, 7, 4, 4, 0, 2, 3, 9, 4, 8, 0, 1, 3, 8, 1, 7, 1, 6
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| "... These are related to properties of dynamical systems with 'period-doubling' oscillations. The ratio of successive differences between period-doubling bifurcation parameters approaches the number 4.669... Period doubling has been discovered in many physical systems before they enter the chaotic regime. Feigenbaum numbers have not been proved to be transcendental but are generally believed to be. ..." [Pickover]
The Feigenbaum delta constant is the convergence ratio {g(k)-g(k-1)}/{g(k+1)-g(k)} of successive period-doubling thresholds g(k) in the continuous map x(n+1)=f(x(n),g) of an interval onto itself. - Lekraj Beedassy (blekraj(AT)yahoo.com), Jan 07 2005
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REFERENCES
| K. Briggs, A precise calculation of the Feigenbaum constants, Math. Comp., 57 (1991), 435-439.
B. Derrida, A. Gervois and Y. Pomeau, Universal metric properties of bifurcations, J. Phys. A 12 (1979), 269-.
S. R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, pp. 65-76
C. A. Pickover, (1993) 'The fifteen most famous transcendental numbers.' "Journal of Recreational Mathematics," 25(1):12.
C. A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," Chapter 44, 'The 15 Most Famous Transcendental Numbers,' Oxford University Press, Oxford, England, 2000, pages 103 - 106.
C. A. Pickover, The Math Book, Sterling, NY, 2009; see p. 462.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Harry J. Smith, Table of n, a(n) for n = 1..1019
A. Krowne, PlanetMath.org, Feigenbaum constant
R. Munafo, Feigenbaum Constant
C. A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," Zentralblatt review
S. Plouffe, Feigenbaum constants
S. Plouffe, Plouffe's Inverter, Feigenbaum constants to 1018 decimal places
Eric Weisstein's World of Mathematics, Feigenbaum Constant
Eric Weisstein's World of Mathematics, Feigenbaum Constant Approximations
Wikipedia, Feigenbaum constant
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EXAMPLE
| 4.669201609102990671853203820466201617258185577475768632745651343004134...
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CROSSREFS
| Cf. A006891 (Feigenbaum reduction parameter), A069544, A102817, A108952, A159766 (continued fraction).
Sequence in context: A173395 A049089 A028327 * A104123 A094078 A016122
Adjacent sequences: A006887 A006888 A006889 * A006891 A006892 A006893
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KEYWORD
| cons,nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), C. L. Mallows (colinm(AT)research.avayalabs.com), Jeffrey Shallit
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EXTENSIONS
| Additional comments from Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 29 2000
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