On the lower Markov spectrum

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.