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EXACT COMPUTATION OF THE BIFURCATION POINT B₄ OF THE LOGISTIC MAP AND THE BAILEY–BROADHURST CONJECTURES

Department of Physics and Computing, Wilfrid Laurier University, N2L 3C5, Waterloo, Ontario, Canada

Ontario Research Centre for Computer Algebra, University of Western Ontario, N6A 5B7, London, Ontario, Canada

and

Centre for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, Campus Plaine, C.P. 231, Boulevard du Triomphe, B-1050, Brussels, Belgium

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https://doi.org/10.1142/S0218127404010709Cited by:15 (Source: Crossref)

Abstract

We compute explicitly the irreducible polynomial corresponding to the bifurcation point B₄ of the logistic map. This settles in the positive recent two conjectures by Bailey and Broadhurst.

Keywords:

References

D. H. Bailey and D. J. Broadhurst, Math. Comput. 70, 1719 (2001). Crossref, Web of Science, Google Scholar
T. Becker and V. Weispfenning , Gröbner Bases , GTM 141 ( Springer-Verlag , NY , 1993 ) . Crossref, Google Scholar
J. M. Borwein and R. M. Corless, Amer. Math. Monthly 106, 889 (1999). Crossref, Web of Science, Google Scholar
J. J. Cannon and C. Playoust , An Introduction to Algebraic Programming in Magma ( School of Mathematics and Statistics, University of Sydney , 1996 ) . Google Scholar
D. Cox , J. Little and D. O'Shea , Ideals, Varieties, and Algorithms , 2nd edn. , Undergraduate Texts in Mathematics ( Springer-Verlag , NY , 1997 ) . Google Scholar