A006890 -id:A006890 - cp's OEIS frontend

A218453 Decimal expansion of the Myrberg point.

1, 4, 0, 1, 1, 5, 5, 1, 8, 9, 0, 9, 2, 0, 5, 0, 6, 0, 0, 5, 2, 3, 8, 2, 6, 7, 8, 7, 8, 9, 3, 8, 6, 1, 2, 9, 2, 2, 2, 6, 3, 0, 8, 0, 4, 3, 3, 9, 7, 3, 1, 9, 6, 0, 8, 9, 3, 7, 2, 6, 1, 4, 9, 6, 6

Offset: 1

Michael Barnsley (Michael.Barnsley(AT)anu.edu.au) and Robert G. Wilson v, Oct 28 2012

"3.3 The sequence of bubbles {B_n}_{n=0...oo} in exercise 3.2 converges to the 'Myreberg point', lambda = 1.40115...." [Barnsley, 2012, p.314]

[Author M. Barnsley consistently spells incorrectly "Myreberg" the name of Pekka J. Myrberg (1892-1976). We leave the original spelling in this citation to improve search results for this phrase. - M. F. Hasler, May 01 2018]

			1.4011551890920506005238267878938612922263...

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 6.8.3, p. 439.

Michael F. Barnsley, Fractals Everywhere, New Edition, Dover Publications, Inc., Mineola, NY, 2012, page 314. ISBN:9780486488707.
Michael F. Barnsley, SuperFractals, Patterns of Nature, Cambridge University Press, United Kingdom, 2006. ISBN 9780521844932.
Michael F. Barnsley, Superfractals (personal web site).
David E. Joyce, Julia and Mandelbrot Sets, Clark University, 1994.
Faber McMullen, The Edge of Chaos (personal web page, updated April 2018).
Wikipedia, Pekka Myrberg.

Cf. A006890, A006891.

More terms from Joerg Arndt, Oct 31 2012
Removed the terms given Oct 31 2012 (these corresponded to the fixed point of f^(2^24) on the real axis). - Joerg Arndt, Jul 17 2016
More terms from Michael Lontke, Irena Rubtsova, and Joerg Arndt, Jan 16 2017

A038123 Beatty sequence for Feigenbaum's constant.

Original entry on oeis.org

4, 9, 14, 18, 23, 28, 32, 37, 42, 46, 51, 56, 60, 65, 70, 74, 79, 84, 88, 93, 98, 102, 107, 112, 116, 121, 126, 130, 135, 140, 144, 149, 154, 158, 163, 168, 172, 177, 182, 186, 191, 196, 200, 205, 210, 214, 219, 224, 228, 233, 238, 242, 247, 252, 256, 261, 266

Offset: 1

Felice Russo

nonn

Index entries for sequences related to Beatty sequences

Cf. A006890.

a = 4.6692016091029906718532038204662; Table[ Floor[n*a], {n, 60}] (* Robert G. Wilson v, Apr 23 2004 *)

a(n)=floor(n*4.6692016609..)

More terms from Robert G. Wilson v, Apr 23 2004

A094078 Decimal expansion of Pi + arctan(e^Pi).

Original entry on oeis.org

4, 6, 6, 9, 2, 0, 1, 9, 3, 1, 8, 5, 9, 9, 0, 7, 7, 3, 1, 5, 5, 8, 8, 5, 2, 6, 2, 6, 0, 8, 2, 3, 9, 7, 8, 7, 4, 5, 5, 7, 3, 1, 5, 7, 1, 2, 5, 4, 9, 3, 2, 2, 9, 8, 0, 1, 2, 6, 8, 7, 1, 9, 7, 4, 3, 6, 0, 8, 5, 1, 7, 6, 6, 1, 2, 1, 9, 2, 2, 6, 2, 5, 4, 2, 5, 9, 0, 4, 6, 9, 9, 2, 7, 3, 1, 4, 8, 8, 0, 9, 1, 0, 3, 8, 3

Offset: 1

Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Apr 30 2004

This is an approximation to the Feigenbaum constant.

			4.669201931859907731558852626...

Eric Weisstein's World of Mathematics, Feigenbaum constant.

Cf. A006890, A039661.

RealDigits[Pi + ArcTan[E^Pi], 10, 120][[1]] (* Robert G. Wilson v, May 04 2004 *)

More terms from Klaus Brockhaus and Robert G. Wilson v, May 03 2004

A187488 Decimal expansion of the Hausdorff dimension of the Feigenbaum attractor and repeller.

Original entry on oeis.org

5, 3, 8, 0, 4, 5, 1, 4, 3, 5, 8, 0, 5, 4, 9, 9, 1, 1, 6, 7, 1, 4, 1, 5, 5, 6

Offset: 0

Paul Muljadi, Mar 10 2011

			0.53804514358054991167141556...

F. Christiansen, P. Cvitanovic, and H. H. Rugh, The spectrum of the period-doubling operator in terms of cycles, J. Phys A, 23 (14) (1990), pp. L713S-L717S.
P. Grassberger, On the Hausdorff dimension of fractal attractors, Journal of Statistical Physics 26 (1981), pp. 173-179.
J. Thurlby, Rigorous calculations of renormalisation fixed points and attractors, PhD thesis, U. Portsmouth, (2021), eq. (5.58)

Cf. A006890.

A306963 Decimal expansion of Feigenbaum's constant 0.399535...

Original entry on oeis.org

3, 9, 9, 5, 3, 5, 2, 8, 0, 5, 2, 3, 1, 3, 4, 4, 8, 9, 8, 5, 7, 5, 8, 0, 4, 6, 8, 6, 3, 3, 6, 9, 3, 7, 1, 9, 4, 3, 3, 5, 4, 4, 2, 8, 0, 4, 6, 6, 9, 5, 2, 7, 2, 7, 5, 1, 7, 0, 7, 3, 0, 4, 4, 9, 1, 2, 4, 3, 8, 0, 1, 6, 6, 0, 8, 8, 3, 8, 0, 4, 2, 9, 8, 1, 8, 4, 4, 5, 9, 4, 8, 7, 4, 1, 8, 1, 2, 6, 6, 8

Offset: 0

N. J. A. Sloane, Mar 18 2019

			0.3995352805231344898575...

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 1.9, pp. 66-67.

M. Campanino, H. Epstein, and D. Ruelle, On Feigenbaum's functional equation g o g (lambda x) + lambda g(x) = 0, Topology, Vol. 21, No. 2 (1982), pp. 125-129.
Artem Dudko and Scott Sutherland, On the Lebesgue measure of the Feigenbaum Julia set, Inventiones mathematicae, Vol. 221 (2020), pp. 167-202.
Mitchell J. Feigenbaum, Quantitative universality for a class of nonlinear transformations, J. Statist. Phys., Vol. 19, No. 1 (1978), pp. 25-52; alternative link; Wayback Machine copy.
Mitchell J. Feigenbaum, The universal metric properties of nonlinear transformations, J. Statist. Phys., Vol. 21, No. 6 (1979), pp. 669-706; CiteSeerX; Wayback Machine copy.
J. Thurlby, Rigorous calculations of renormalisation fixed points and attractors, PhD thesis, U. Portsmouth, (2021). 400 digits in section 3.8.

Cf. A006890, A006891, A119277, etc.

Equals 1/A006891. - Stefano Spezia, Nov 23 2024

More terms from Dudko and Sutherland (2020) added by Amiram Eldar, May 15 2021

a(22)-a(99) from Stefano Spezia, Nov 23 2024

cp's OEIS Frontend

A218453 Decimal expansion of the Myrberg point.

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A038123 Beatty sequence for Feigenbaum's constant.

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A094078 Decimal expansion of Pi + arctan(e^Pi).

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A187488 Decimal expansion of the Hausdorff dimension of the Feigenbaum attractor and repeller.

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A306963 Decimal expansion of Feigenbaum's constant 0.399535...

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