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The geometric unfolding of recurrence relations

Published online by Cambridge University Press:  08 October 2020

Stan Dolan
Stan Dolan*
Affiliation:
126A Harpenden Road, St Albans AL3 6BZ e-mail: [email protected]
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Extract

In 1942 R. C. Lyness challenged readers of the Gazette to find a recurrence relation of order 2 which would generate a cycle of period 7 for almost all initial values [1].

Type
Articles
Information
The Mathematical Gazette , Volume 104 , Issue 561 , November 2020 , pp. 403 - 411
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Copyright
© Mathematical Association 2020

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References

Lyness, R. C., Cycles, Math. Gaz. 26 (February 1942) p. 62.CrossRefGoogle Scholar
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Griffiths, J., Lyness cycles, elliptic curves and Hikorsky triples, accessed April 2020 at ueaeprints.uea.ac.uk/id/eprint/38238/1/2012GriffithsJMSc.pdfGoogle Scholar
Janowski, E. J., Kocic, V. L., Ladas, G., and Schultz, S. W., Global behavior of solutions of xn + 1 = max {xn, A} / xn − 1, Proceedings of the First International Conference on Difference Equations (May 1994), San Antonio, Gordon and Breach, Basel (1995).Google Scholar
Northshield, S., Tropical cycles, Math. Gaz. 104 (July 2020), pp. 225–234.10.1017/mag.2020.44CrossRefGoogle Scholar