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Quadratic Irrationals in the Lower Lagrange Spectrum
Published online by Cambridge University Press: 20 November 2018
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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.
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- Copyright © Canadian Mathematical Society 1973
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