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2013•Journal of MathematicsOpen access

Dimension Estimates for Certain Sets of Infinite Complex Continued Fractions

Jörg Neunhäuserer

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Abstract

We prove upper and lower estimates on the Hausdorff dimension of sets of infinite complex continued fractions with finitely many prescribed Gaussian integers. Particulary we will conclude that the dimension of theses sets is not zero or two and there are such sets with dimension greater than one and smaller than one.

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We prove upper and lower estimates on the Hausdorff dimension of sets of infinite complex continued fractions with finitely many prescribed Gaussian integers. Particulary we will conclude that the dimension of theses sets is not zero or two and there are such sets with dimension greater than one and smaller than one.

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Available abstract

We prove upper and lower estimates on the Hausdorff dimension of sets of infinite complex continued fractions with finitely many prescribed Gaussian integers. Particulary we will conclude that the dimension of theses sets is not zero or two and there are such sets with dimension greater than one and smaller than one.

Key concepts: Mathematics, Hausdorff dimension, Packing dimension, Dimension (graph theory), Zero (linguistics), Minkowski–Bouligand dimension, Dimension function, Combinatorics

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