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On the lower Markov spectrum

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Abstract

C. Hightower found two infinite sequences of gaps in the Markov spectrum, (α n , β n ) and (γ n , δ n ) with β n and γ n both Markov elements, converging to\(1 + \sqrt 5 \). This paper exhibits Markov elements α * n and δ * n such that, for alln ⩾ 1, (α * n , β n ) and (γ n δ * n ) are gaps in the Markov spectrum. Other results include showing that, for alln ⩾ 1, β n is completely isolated, while the other endpoints of the gaps are limit points in the Markov spectrum.

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  1. Mathematics Department, The Ohio State University, 231 West 18th Avenue, 43210, Columbus, OH, USA

    Mary E. Gbur

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  1. Mary E. Gbur
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Gbur, M.E. On the lower Markov spectrum. Monatshefte für Mathematik 81, 95–107 (1976). https://doi.org/10.1007/BF01301234

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  • DOI: https://doi.org/10.1007/BF01301234

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