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Quadratic Irrationals in the Lower Lagrange Spectrum

Published online by Cambridge University Press:  20 November 2018

Nancy Davis  and
J. R. Kinney
Nancy Davis
Affiliation:
University of Chicago, Chicago, Illinois
J. R. Kinney
Affiliation:
Michigan State University, East Lansing, Michigan
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We let , where the xi are positive integers and i ∈ N, the set of all integers. We define , where where . We let = [0; x1, x2, … ] where

We let

and define

The range of L(ξ) is known as the Lagrange spectrum and the range of M(ξ) as the Markov spectrum. It is known that both are closed and that the Markov spectrum includes the Lagrange spectrum.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 3 , June 1973 , pp. 578 - 584
Copyright
Copyright © Canadian Mathematical Society 1973

References

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