The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A181917 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A181917

The value of r at the bifurcation point of the first period-11 cycle of the logistic map f(x) = r*x*(1 - x).
(history; published version)

#17 by N. J. A. Sloane at Mon Apr 02 23:07:48 EDT 2012

STATUS

proposed

approved

#16 by Cheng Zhang at Mon Apr 02 22:24:40 EDT 2012

STATUS

editing

proposed

#15 by Cheng Zhang at Mon Apr 02 22:23:49 EDT 2012

LINKS

Cheng Zhang, <a href="/A181917/a181917.txt">the minimal polynomial of T = r*(r-2)</a>

#14 by Cheng Zhang at Mon Apr 02 22:17:05 EDT 2012

COMMENTS

Root of a degree 1023*2 = 2046 polynomial.

CROSSREFS

Cf. A086178, A086179, A086180, A086181, A091517, A118452, A118453, A118746, A181906, A181907, A181909, A181910, A181911, A181912, A181913, A181915, A181916, A181918, A181919.

#13 by T. D. Noe at Mon Apr 02 20:10:59 EDT 2012

NAME

The value of r at the bifurcation point of the first period-11 cycle of the logistic map f(x) = r*x*(1 - x).

CROSSREFS

Cf. A086178, A086179, A086180, A086181, A091517, A118452, A181906, A181907, A181909, A181910, A181911, A181912, A181913, A181915, A181916, A181918, A181919.

STATUS

proposed

editing

#12 by Joerg Arndt at Mon Apr 02 05:56:46 EDT 2012

STATUS

editing

proposed

Discussion

Mon Apr 02

06:12

Cheng Zhang: For the bifurcation point, almost yes. But the leading coefficient might be -1. So not exactly the minimal polynomial.
For the onset point, there are generally several factors in the polynomials (see the attached file), so definitely not the minimal polynomial.

#11 by Joerg Arndt at Mon Apr 02 05:55:30 EDT 2012

LINKS

Cheng Zhang, <a href="/A181917/a181917.txt">the minimal polynomial for of T = r*(r-2)</a>

STATUS

proposed

editing

Discussion

Mon Apr 02

05:56

Joerg Arndt: The file does contain the minimal polynomial followed by the roots, correct?

#10 by Cheng Zhang at Mon Apr 02 05:49:05 EDT 2012

STATUS

editing

proposed

#9 by Cheng Zhang at Mon Apr 02 05:48:53 EDT 2012

NAME

Bifurcation The value of r at the bifurcation point of the first period-11 cycle of the logistic map f(x) = r *x *(1 - x)

COMMENTS

Root of a degree 1023x2 1023*2 = 2046 polynomial

LINKS

Cheng Zhang, <a href="/A181917/a181917.txt">The the polynomial for T = r*(r-2)</a>

STATUS

proposed

editing

#8 by Cheng Zhang at Mon Apr 02 01:00:19 EDT 2012

STATUS

editing

proposed