

A256720


Decimal expansion of the location of the far bifurcation cusp in the Zeeman catastrophe machine.


2



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

1,1


COMMENTS

Largest root of 10*x^227*x+6, equal to (27+sqrt(489))/20 (Poston 1978).
Applies to the 'classical' Zeeman machine with a disk of diameter 1 and the distance between the pivot and the fixed point equal to 2. With respect to the pivot, the near and far bifurcation cusps are located on opposite side the fixed point. This constant is the far cusp's distance from the pivot.


REFERENCES

T. Poston and I. Stewart, Catastrophe Theory and its Applications, Pitman Publishing Ltd, 1978, Chapter 5, page 76.
E. C. Zeeman, Catastrophe Theory, Scientific American, April 1976, pages 6570, 7583.


LINKS

Stanislav Sykora, Table of n, a(n) for n = 1..2000
D. Cross, Zeeman's Catastrophe Machine in HTML 5
The Nonlinear Dynamics Group at Drexel University, Zeeman's Catastrophe Machine
Wikipedia, Catastrophe theory


EXAMPLE

2.455667219374799046502040536096042680896241972136288067754970...


PROG

(PARI) a=(27+sqrt(489))/20 \\ Use \p 2020, and keep 2000 digits


CROSSREFS

Cf. A256719 (near bifurcation cusp).
Sequence in context: A131813 A083038 A061008 * A091988 A023824 A081252
Adjacent sequences: A256717 A256718 A256719 * A256721 A256722 A256723


KEYWORD

nonn,cons


AUTHOR

Stanislav Sykora, Apr 09 2015


STATUS

approved



