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In this paper we consider the times-q map on the unit interval as a subshiftof finite type by identifying each number with its base q expansion, and westudy certain non-dense orbits of this system where no element of the orbit issmaller than some fixed parameter c. The Hausdorff dimension of these orbitscan be calculated using the spectral radius of the transition matrix of thecorresponding subshift, and using simple methods based on Euclidean division inthe integers, we completely characterize the characteristic polynomials ofthese matrices as well as give the value of the spectral radius for certainvalues of c. It is known through work of Urbanski and Nilsson that theHausdorff dimension of the orbits men- tioned above as a map of c is continuousand constant almost everywhere, and as a new result we give some asymptoticresults on how this map behaves as q goes to infinity,

On lower bounded orbits of the times-q map